Details

analyze926.0ms (18.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
26.2%	73.5%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
1.0ms	23×	body	80	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify313.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (303.0ms)

Iter	Nodes	Cost
0	5592	16

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 1.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
2.7b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
26×	`add-cube-cbrt_binary64`
22×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`pow1_binary64` `associate-/r/_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

2 → 102

Calls

2 calls:

14.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

series31.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
13.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5026	1767

prune91.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	8	109

Merged error: 0b

Counts

109 → 8

Compiler

Compiled 2122 to 478 computations (77.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a t))
0.5b	(cbrt.f64 (-.f64 a t))
0.5b	(cbrt.f64 (-.f64 a t))
5.2b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
46×	`associate-r_binary64`
42×	`cbrt-prod_binary64`
28×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
20×	`cbrt-div_binary64`
18×	`add-cbrt-cube_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
15×	`associate-l_binary64`
10×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64`
5×	`frac-times_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `pow1/3_binary64` `associate-l/_binary64`
2×	`div-inv_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 136

Calls

4 calls:

32.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
5.0ms	(cbrt.f64 (-.f64 a t))
3.0ms	(cbrt.f64 (-.f64 a t))
3.0ms	(cbrt.f64 (-.f64 a t))

series107.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
27.0ms	(cbrt.f64 (-.f64 a t))
25.0ms	(cbrt.f64 (-.f64 a t))
25.0ms	(cbrt.f64 (-.f64 a t))

simplify132.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5102	3468

prune89.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	149	7	156

Merged error: 0b

Counts

156 → 7

Compiler

Compiled 4359 to 806 computations (81.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
4.6b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
4.6b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
4.6b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite84.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

333×	`*-un-lft-identity_binary64`
277×	`cbrt-prod_binary64`
273×	`add-sqr-sqrt_binary64`
229×	`times-frac_binary64`
106×	`distribute-lft-out--_binary64`
93×	`add-cube-cbrt_binary64`
78×	`difference-of-squares_binary64`
58×	`swap-sqr_binary64`
34×	`associate-r_binary64` `associate-l_binary64`
14×	`associate-/r/_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64` `unswap-sqr_binary64`
7×	`cbrt-div_binary64` `flip3--_binary64` `div-inv_binary64` `flip--_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `associate-r/_binary64` `pow-plus_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 276

Calls

4 calls:

34.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
9.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
7.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
7.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

series276.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
66.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
66.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
64.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

simplify156.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4918	8771
1	4918	8771

prune179.0ms (3.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	288	7	295

Merged error: 0b

Counts

295 → 7

Compiler

Compiled 11644 to 1863 computations (84% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.7b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
5.8b	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
5.8b	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
5.8b	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`cbrt-div_binary64` `pow1/3_binary64` `associate-l_binary64` `cbrt-prod_binary64`
2×	`cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

14.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
12.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
9.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
9.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

series200.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
60.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
60.0ms	(cbrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
18.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5073	1426

prune47.0ms (1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	92	7	99

Merged error: 0b

Counts

99 → 7

Compiler

Compiled 3669 to 460 computations (87.5% saved)

regimes530.0ms (10.8%)

Compiler: Compiled 1319 to 873 computations (33.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	34
1	28	34

end0.0ms (0%)

sample1.4s (28.7%)

Algorithm

1×

intervals

Results

294.0ms	7999×	body	80	valid
25.0ms	728×	body	80	invalid
0.0ms	1×	body	1280	valid

Compiler

Compiled 213 to 133 computations (37.6% saved)

Details

analyze926.0ms (18.8%)

sample25.0ms (0.5%)

simplify313.0ms (6.3%)

prune6.0ms (0.1%)

localize8.0ms (0.2%)

rewrite27.0ms (0.6%)

series31.0ms (0.6%)

simplify85.0ms (1.7%)

prune91.0ms (1.9%)

localize12.0ms (0.2%)

rewrite52.0ms (1%)

series107.0ms (2.2%)

simplify132.0ms (2.7%)

prune89.0ms (1.8%)

localize12.0ms (0.2%)

rewrite84.0ms (1.7%)

series276.0ms (5.6%)

simplify156.0ms (3.2%)

prune179.0ms (3.6%)

localize12.0ms (0.3%)

rewrite47.0ms (1%)

series200.0ms (4.1%)

simplify62.0ms (1.3%)

prune47.0ms (1%)

regimes530.0ms (10.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (28.7%)

Profiling