Details

analyze257.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample64.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	80×	body	1024	valid
13.0ms	40×	body	2048	valid
8.0ms	37×	body	512	valid
3.0ms	75×	body	128	valid
3.0ms	22×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify168.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune2.0ms (0%)

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: 54.6b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.5b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.7b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
16.8b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
4×	`log-prod_binary64_2551` `add-exp-log_binary64_2503`
3×	`flip3-+_binary64_2468` `sqrt-prod_binary64_2481` `flip-+_binary64_2439` `add-cbrt-cube_binary64_2501`
2×	`log-div_binary64_2552` `distribute-lft-out_binary64_2416` `sqrt-div_binary64_2482`
1×	`+-commutative_binary64_2395` `log-pow_binary64_2554` `sum-log_binary64_2556` `pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483` `rem-log-exp_binary64_2506`

Counts

3 → 42

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series180.0ms (3%)

Counts

3 → 9

Calls

3 calls:

91.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
56.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
33.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4924	862
1	4924	862

prune70.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 0.0b

Counts

52 → 6

Compiler

Compiled 849 to 567 computations (33.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
22.3b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2487`
15×	`associate-l_binary64_2406`
14×	`add-exp-log_binary64_2503`
11×	`*-un-lft-identity_binary64_2465` `add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500`
10×	`associate-r_binary64_2405`
8×	`add-cbrt-cube_binary64_2501` `unpow-prod-down_binary64_2544`
7×	`unswap-sqr_binary64_2433`
6×	`prod-exp_binary64_2514`
4×	`cube-prod_binary64_2493` `sqr-pow_binary64_2437` `pow1_binary64_2526`
2×	`*-commutative_binary64_2396` `sum-log_binary64_2556` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `diff-log_binary64_2557` `cbrt-unprod_binary64_2498`
1×	`flip3-+_binary64_2468` `unpow3_binary64_2531` `+-commutative_binary64_2395` `flip--_binary64_2440` `flip-+_binary64_2439` `sub-neg_binary64_2458` `cube-mult_binary64_2495` `cancel-sign-sub-inv_binary64_2431` `associate--l+_binary64_2402` `flip3--_binary64_2469`

Counts

4 → 81

Calls

4 calls:

7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
7.0ms	(*.f64 3/40 (pow.f64 x 5))
7.0ms	(*.f64 (pow.f64 x 3) 1/6)
3.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series323.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
65.0ms	(*.f64 3/40 (pow.f64 x 5))
58.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
45.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5018	1208

prune102.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Merged error: 0.0b

Counts

99 → 6

Compiler

Compiled 1741 to 1349 computations (22.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.2b	(/.f64 1/8 (pow.f64 x 3))
10.5b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
19.2b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite125.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64_2465`
73×	`times-frac_binary64_2471` `add-sqr-sqrt_binary64_2487`
47×	`add-cube-cbrt_binary64_2500`
26×	`unpow-prod-down_binary64_2544`
19×	`associate-/r*_binary64_2409`
15×	`add-exp-log_binary64_2503`
14×	`cube-prod_binary64_2493`
11×	`log-prod_binary64_2551`
10×	`difference-of-squares_binary64_2434` `sqr-pow_binary64_2437`
9×	`add-log-exp_binary64_2504`
8×	`add-cbrt-cube_binary64_2501`
6×	`distribute-lft-out--_binary64_2417` `div-exp_binary64_2516` `distribute-lft-out_binary64_2416` `associate-/l*_binary64_2410` `frac-sub_binary64_2474`
5×	`log-div_binary64_2552` `cancel-sign-sub-inv_binary64_2431` `pow1_binary64_2526`
4×	`unpow3_binary64_2531` `cube-mult_binary64_2495`
2×	`flip3-+_binary64_2468` `flip--_binary64_2440` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `div-inv_binary64_2462` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `flip3--_binary64_2469` `frac-add_binary64_2473`
1×	`associate--r+_binary64_2401` `log-pow_binary64_2554` `sum-log_binary64_2556` `sub-neg_binary64_2458` `rem-log-exp_binary64_2506`

Counts

4 → 164

Calls

4 calls:

48.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
48.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series239.0ms (4%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
59.0ms	(/.f64 1/16 (pow.f64 x 5))
52.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
49.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4966	3700
1	4966	3700

prune265.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	175	7	182

Merged error: 0.0b

Counts

182 → 7

Compiler

Compiled 4281 to 3406 computations (20.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

11.9b	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
19.2b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
19.2b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
19.2b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite213.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_2465`
60×	`add-sqr-sqrt_binary64_2487`
34×	`times-frac_binary64_2471`
20×	`difference-of-squares_binary64_2434`
19×	`add-log-exp_binary64_2504`
15×	`cancel-sign-sub-inv_binary64_2431`
14×	`distribute-lft-out_binary64_2416`
12×	`distribute-lft-out--_binary64_2417` `frac-sub_binary64_2474`
11×	`cbrt-prod_binary64_2496`
8×	`add-cube-cbrt_binary64_2500`
6×	`diff-log_binary64_2557`
5×	`cbrt-div_binary64_2497`
4×	`flip3-+_binary64_2468` `flip--_binary64_2440` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `cube-prod_binary64_2493` `add-cbrt-cube_binary64_2501` `unpow-prod-down_binary64_2544` `sqr-pow_binary64_2437` `pow1_binary64_2526` `flip3--_binary64_2469` `frac-add_binary64_2473`
3×	`associate--r+_binary64_2401` `sum-log_binary64_2556` `sub-neg_binary64_2458`
1×	`pow1/3_binary64_2547`

Counts

4 → 111

Calls

4 calls:

50.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
49.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
46.0ms	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
46.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series270.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
51.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
48.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
46.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4902	4251
1	4902	4251

prune549.0ms (9.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	123	7	130

Merged error: 0.0b

Counts

130 → 7

Compiler

Compiled 7611 to 6276 computations (17.5% saved)

regimes178.0ms (3%)

Compiler: Compiled 1445 to 1117 computations (22.7% saved)

bsearch36.0ms (0.6%)

Steps

Iters	Range		Point
9	7.566239810847678e-05	80.7257126355526	0.9534000391305874
8	-30.19310355872626	-0.10476816923778465	-1.060029406698972

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.5s (41.8%)

Algorithm

1×

intervals

Results

957.0ms	2523×	body	1024	valid
398.0ms	1221×	body	2048	valid
260.0ms	1249×	body	512	valid
106.0ms	2311×	body	128	valid
74.0ms	654×	body	256	valid
20.0ms	42×	body	4096	valid

Compiler

Compiled 491 to 382 computations (22.2% saved)

Details

analyze257.0ms (4.3%)

sample64.0ms (1.1%)

simplify168.0ms (2.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite23.0ms (0.4%)

series180.0ms (3%)

simplify56.0ms (0.9%)

prune70.0ms (1.2%)

localize10.0ms (0.2%)

rewrite31.0ms (0.5%)

series323.0ms (5.4%)

simplify65.0ms (1.1%)

prune102.0ms (1.7%)

localize12.0ms (0.2%)

rewrite125.0ms (2.1%)

series239.0ms (4%)

simplify84.0ms (1.4%)

prune265.0ms (4.5%)

localize18.0ms (0.3%)

rewrite213.0ms (3.6%)

series270.0ms (4.6%)

simplify100.0ms (1.7%)

prune549.0ms (9.3%)

regimes178.0ms (3%)

bsearch36.0ms (0.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.5s (41.8%)

Profiling