Details

analyze128.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample35.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	208×	body	80	valid
5.0ms	19×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	13×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	7×	body	160	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5223	43

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 25.3b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.8b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

21.9b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite78.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/l/_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
5×	`add-log-exp_binary64`
4×	`frac-times_binary64`
3×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

3 → 111

Calls

3 calls:

34.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

25.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

15.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series191.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

99.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

73.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

19.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify104.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5572	5261

prune187.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	9	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Merged error: 5.7b

Counts

121 → 9

Compiler

Compiled 5352 to 2819 computations (47.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
2.8b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

rewrite117.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac_binary64`
290×	`*-un-lft-identity_binary64`
211×	`add-sqr-sqrt_binary64`
140×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
44×	`distribute-lft-out_binary64`
31×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
26×	`associate-/l*_binary64`
24×	`associate-/r/_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-l_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `div-sub_binary64` `prod-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 295

Calls

4 calls:

39.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
27.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
24.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series232.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
78.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
42.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
18.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify174.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5051	13438

prune601.0ms (7.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	303	4	307
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	307	9	316

Merged error: 5.7b

Counts

316 → 9

Compiler

Compiled 14688 to 7757 computations (47.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
2.8b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

rewrite144.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

306×	`times-frac_binary64`
275×	`*-un-lft-identity_binary64`
196×	`add-sqr-sqrt_binary64`
133×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
44×	`distribute-lft-out_binary64`
27×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-/r/_binary64`
21×	`associate-/l*_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
12×	`cbrt-prod_binary64`
11×	`div-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-/r_binary64` `associate-l*_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64`
2×	`cbrt-div_binary64` `cube-div_binary64` `div-sub_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `rem-cbrt-cube_binary64` `associate-r/_binary64` `pow1/3_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 278

Calls

4 calls:

43.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
34.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
29.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
21.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))

series317.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
97.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
79.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
44.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))

simplify159.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4995	13897
1	4995	13897

prune675.0ms (8.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	285	5	290
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	289	10	299

Merged error: 5.7b

Counts

299 → 10

Compiler

Compiled 15062 to 8371 computations (44.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.2b	(pow.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3) 1/3)
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
2.8b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

rewrite139.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

306×	`times-frac_binary64`
276×	`*-un-lft-identity_binary64`
197×	`add-sqr-sqrt_binary64`
134×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
44×	`distribute-lft-out_binary64`
27×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-/r/_binary64`
21×	`associate-/l*_binary64`
20×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
15×	`unpow-prod-down_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
11×	`div-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-/r_binary64` `associate-l*_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cube-prod_binary64`
2×	`pow-to-exp_binary64` `sqr-pow_binary64` `div-sub_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-r/_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `unpow3_binary64` `unpow1/3_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 284

Calls

4 calls:

40.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
34.0ms	(pow.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3) 1/3)
29.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
20.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))

series988.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

772.0ms	(pow.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3) 1/3)
95.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
78.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
42.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))

simplify162.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5279	14138

prune686.0ms (9.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	293	3	296
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	295	11	306

Merged error: 4.4b

Counts

306 → 11

Compiler

Compiled 15065 to 8491 computations (43.6% saved)

regimes251.0ms (3.3%)

Compiler: Compiled 2088 to 1428 computations (31.6% saved)

bsearch61.0ms (0.8%)

Steps

Iters	Range		Point
10	1.2768700373779192e+116	5.4317174979087905e+129	8.555499500646715e+121
7	1.1376274474741083e+81	2.6892054372336194e+82	1.3578860986539075e+81

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	79	152
1	79	152

end0.0ms (0%)

sample2.0s (26.1%)

Algorithm

1×

intervals

Results

344.0ms	6324×	body	80	valid
167.0ms	8000×	pre	80	true
149.0ms	521×	body	1280	valid
128.0ms	588×	body	640	valid
59.0ms	366×	body	320	valid
21.0ms	201×	body	160	valid

Compiler

Compiled 659 to 448 computations (32% saved)

Details

analyze128.0ms (1.7%)

sample35.0ms (0.5%)

simplify85.0ms (1.1%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

rewrite78.0ms (1%)

series191.0ms (2.5%)

simplify104.0ms (1.4%)

prune187.0ms (2.5%)

localize16.0ms (0.2%)

rewrite117.0ms (1.5%)

series232.0ms (3.1%)

simplify174.0ms (2.3%)

prune601.0ms (7.9%)

localize16.0ms (0.2%)

rewrite144.0ms (1.9%)

series317.0ms (4.2%)

simplify159.0ms (2.1%)

prune675.0ms (8.9%)

localize20.0ms (0.3%)

rewrite139.0ms (1.8%)

series988.0ms (13.1%)

simplify162.0ms (2.1%)

prune686.0ms (9.1%)

regimes251.0ms (3.3%)

bsearch61.0ms (0.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.0s (26.1%)

Profiling