Details

analyze276.0ms (5.5%)

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)

sample71.0ms (1.4%)

Algorithm

1×

intervals

Results

32.0ms	83×	body	1024	valid
16.0ms	48×	body	2048	valid
10.0ms	45×	body	512	valid
3.0ms	61×	body	128	valid
2.0ms	18×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify168.0ms (3.3%)

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: 53.5b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.5b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2831`
6×	`add-sqr-sqrt_binary64_2853`
5×	`pow1_binary64_2892` `add-cube-cbrt_binary64_2866` `add-log-exp_binary64_2870`
4×	`log-prod_binary64_2917` `add-exp-log_binary64_2869`
3×	`flip3-+_binary64_2834` `add-cbrt-cube_binary64_2867` `sqrt-prod_binary64_2847` `flip-+_binary64_2805`
2×	`sqrt-div_binary64_2848` `distribute-lft-out_binary64_2782` `log-div_binary64_2918`
1×	`rem-sqrt-square_binary64_2844` `pow1/2_binary64_2911` `log-pow_binary64_2920` `+-commutative_binary64_2761` `rem-log-exp_binary64_2872` `sqrt-pow1_binary64_2849` `sum-log_binary64_2922`

Counts

3 → 42

Calls

3 calls:

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

series184.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

89.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
61.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
34.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4924	862
1	4924	862

prune179.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

Compiler

Compiled 2181 to 1587 computations (27.2% 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)
19.8b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2853`
15×	`associate-l_binary64_2772`
14×	`add-exp-log_binary64_2869`
11×	`add-cube-cbrt_binary64_2866` `add-log-exp_binary64_2870` `*-un-lft-identity_binary64_2831`
10×	`associate-r_binary64_2771`
8×	`unpow-prod-down_binary64_2910` `add-cbrt-cube_binary64_2867`
7×	`unswap-sqr_binary64_2799`
6×	`prod-exp_binary64_2880`
4×	`pow1_binary64_2892` `sqr-pow_binary64_2803` `cube-prod_binary64_2859`
2×	`pow-exp_binary64_2899` `cbrt-unprod_binary64_2864` `*-commutative_binary64_2762` `diff-log_binary64_2923` `pow-to-exp_binary64_2900` `sum-log_binary64_2922`
1×	`flip3-+_binary64_2834` `cube-mult_binary64_2861` `flip3--_binary64_2835` `sub-neg_binary64_2824` `+-commutative_binary64_2761` `cancel-sign-sub-inv_binary64_2797` `flip--_binary64_2806` `associate--l+_binary64_2768` `flip-+_binary64_2805` `unpow3_binary64_2897`

Counts

4 → 81

Calls

4 calls:

8.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
7.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))
3.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series344.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
59.0ms	(*.f64 3/40 (pow.f64 x 5))
56.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
51.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5018	1208

prune101.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	93	4	97

Merged error: 0b

Counts

97 → 4

Compiler

Compiled 1704 to 1320 computations (22.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/8 (pow.f64 x 3))
0.1b	(/.f64 1/16 (pow.f64 x 5))
12.9b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
22.8b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite116.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64_2831`
73×	`add-sqr-sqrt_binary64_2853` `times-frac_binary64_2837`
47×	`add-cube-cbrt_binary64_2866`
26×	`unpow-prod-down_binary64_2910`
19×	`associate-/r*_binary64_2775`
15×	`add-exp-log_binary64_2869`
14×	`cube-prod_binary64_2859`
11×	`log-prod_binary64_2917`
10×	`sqr-pow_binary64_2803` `difference-of-squares_binary64_2800`
9×	`add-log-exp_binary64_2870`
8×	`add-cbrt-cube_binary64_2867`
6×	`distribute-lft-out_binary64_2782` `frac-sub_binary64_2840` `distribute-lft-out--_binary64_2783` `div-exp_binary64_2882` `associate-/l*_binary64_2776`
5×	`pow1_binary64_2892` `log-div_binary64_2918` `cancel-sign-sub-inv_binary64_2797`
4×	`cube-mult_binary64_2861` `unpow3_binary64_2897`
2×	`frac-2neg_binary64_2842` `pow-exp_binary64_2899` `flip3-+_binary64_2834` `div-inv_binary64_2828` `cbrt-undiv_binary64_2865` `flip3--_binary64_2835` `diff-log_binary64_2923` `frac-add_binary64_2839` `pow-to-exp_binary64_2900` `flip--_binary64_2806` `flip-+_binary64_2805` `clear-num_binary64_2830`
1×	`log-pow_binary64_2920` `associate--r+_binary64_2767` `sub-neg_binary64_2824` `rem-log-exp_binary64_2872` `sum-log_binary64_2922`

Counts

4 → 164

Calls

4 calls:

44.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
43.0ms	(-.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))

series241.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
60.0ms	(/.f64 1/16 (pow.f64 x 5))
53.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
47.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4966	3700
1	4966	3700

prune278.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	176	4	180

Merged error: 0b

Counts

180 → 4

Compiler

Compiled 4193 to 3334 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.1b	(/.f64 1/8 (pow.f64 x 3))
10.9b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite90.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`times-frac_binary64_2837` `*-un-lft-identity_binary64_2831`
52×	`add-cube-cbrt_binary64_2866` `add-sqr-sqrt_binary64_2853`
42×	`associate-+r+_binary64_2763`
40×	`cancel-sign-sub-inv_binary64_2797`
21×	`unpow-prod-down_binary64_2910` `cube-prod_binary64_2859`
15×	`add-log-exp_binary64_2870`
12×	`associate-/r*_binary64_2775`
10×	`add-exp-log_binary64_2869`
9×	`distribute-lft-out_binary64_2782`
7×	`sqr-pow_binary64_2803` `cube-mult_binary64_2861` `unpow3_binary64_2897`
6×	`log-prod_binary64_2917` `add-cbrt-cube_binary64_2867`
5×	`pow1_binary64_2892` `sum-log_binary64_2922`
4×	`distribute-lft-out--_binary64_2783`
3×	`flip3-+_binary64_2834` `div-exp_binary64_2882` `flip-+_binary64_2805` `associate-/l*_binary64_2776`
2×	`div-inv_binary64_2828` `diff-log_binary64_2923` `log-div_binary64_2918` `+-commutative_binary64_2761`
1×	`frac-2neg_binary64_2842` `pow-exp_binary64_2899` `log-pow_binary64_2920` `cbrt-undiv_binary64_2865` `sub-neg_binary64_2824` `associate-+r-_binary64_2765` `pow-to-exp_binary64_2900` `rem-log-exp_binary64_2872` `associate--l+_binary64_2768` `clear-num_binary64_2830`

Counts

4 → 153

Calls

4 calls:

32.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
29.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
6.0ms	(+.f64 x (/.f64 1/2 x))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series229.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
57.0ms	(/.f64 1/8 (pow.f64 x 3))
54.0ms	(+.f64 x (/.f64 1/2 x))
44.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4992	2477
1	4992	2477

prune200.0ms (4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	165	4	169

Merged error: 0b

Counts

169 → 4

Compiler

Compiled 3452 to 2503 computations (27.5% saved)

regimes22.0ms (0.4%)

Compiler: Compiled 56 to 47 computations (16.1% saved)

bsearch42.0ms (0.8%)

Steps

Iters	Range		Point
9	0.6814830664350081	219361.26943641825	0.9586458855915625
9	-3.996062453584732	-1.8155029574833036e-07	-1.0620143966736946

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%)

sample2.1s (42.3%)

Algorithm

1×

intervals

Results

943.0ms	2525×	body	1024	valid
403.0ms	1244×	body	2048	valid
262.0ms	1254×	body	512	valid
109.0ms	2313×	body	128	valid
71.0ms	628×	body	256	valid
20.0ms	36×	body	4096	valid

Compiler

Compiled 139 to 111 computations (20.1% saved)

Details

analyze276.0ms (5.5%)

sample71.0ms (1.4%)

simplify168.0ms (3.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite21.0ms (0.4%)

series184.0ms (3.7%)

simplify61.0ms (1.2%)

prune179.0ms (3.5%)

localize10.0ms (0.2%)

rewrite31.0ms (0.6%)

series344.0ms (6.8%)

simplify64.0ms (1.3%)

prune101.0ms (2%)

localize14.0ms (0.3%)

rewrite116.0ms (2.3%)

series241.0ms (4.8%)

simplify89.0ms (1.8%)

prune278.0ms (5.5%)

localize10.0ms (0.2%)

rewrite90.0ms (1.8%)

series229.0ms (4.5%)

simplify54.0ms (1.1%)

prune200.0ms (4%)

regimes22.0ms (0.4%)

bsearch42.0ms (0.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (42.3%)

Profiling