Details

analyze720.0ms (7.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	154
1	43	154
0	4	4
1	4	4

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample23.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune3.0ms (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

Error

26.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.6b	(+.f64 (.f64 a c) (.f64 b d))
25.4b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite106.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

25.9b

Rules

10×	`add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
9×	`times-frac_binary64_2812`
4×	`add-exp-log_binary64_2844` `add-log-exp_binary64_2845` `add-cbrt-cube_binary64_2842`
3×	`flip3-+_binary64_2809` `flip-+_binary64_2780` `associate-/l_binary64_2751` `associate-/r_binary64_2750`
2×	`pow1_binary64_2867` `associate-/l/_binary64_2753` `associate-/r/_binary64_2752`
1×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

2 → 42

Calls

2 calls:

13.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 1203 to 160 computations (86.7% saved)

series556.0ms (6.1%)

Error

5.9b

Counts

2 → 54

Calls

2 calls:

382.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
134.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 1956 to 1221 computations (37.6% saved)

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5038	1977

prune80.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Error

5.8b

Counts

97 → 10

Compiler

Compiled 2037 to 312 computations (84.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 d b) (.f64 c a))
16.7b	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
27.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
27.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite130.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

23×	`add-sqr-sqrt_binary64_2828`
21×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
18×	`sqrt-prod_binary64_2822` `times-frac_binary64_2812`
6×	`pow1_binary64_2867` `add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `sqrt-div_binary64_2823` `associate-/r*_binary64_2750`
5×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
3×	`associate-/l*_binary64_2751`
2×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `associate-/l/_binary64_2753` `associate-/r/_binary64_2752`
1×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 84

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 d b) (.f64 c a))

Compiler

Compiled 3211 to 343 computations (89.3% saved)

series1.2s (13%)

Error

5.8b

Counts

4 → 95

Calls

4 calls:

569.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
208.0ms	(+.f64 (.f64 d b) (.f64 c a))
154.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
123.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 5888 to 3115 computations (47.1% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4980	3730
1	4980	3730

prune162.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	178	11	189

Error

5.8b

Counts

189 → 11

Compiler

Compiled 5500 to 839 computations (84.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 d b) (.f64 c a))
16.7b	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
27.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
27.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite143.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

23×	`add-sqr-sqrt_binary64_2828`
21×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
18×	`sqrt-prod_binary64_2822` `times-frac_binary64_2812`
6×	`pow1_binary64_2867` `add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `sqrt-div_binary64_2823` `associate-/r*_binary64_2750`
5×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
3×	`associate-/l*_binary64_2751`
2×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `associate-/l/_binary64_2753` `associate-/r/_binary64_2752`
1×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 84

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
8.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 d b) (.f64 c a))

Compiler

Compiled 3379 to 516 computations (84.7% saved)

series870.0ms (9.6%)

Error

5.8b

Counts

4 → 95

Calls

4 calls:

396.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
148.0ms	(+.f64 (.f64 d b) (.f64 c a))
120.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
119.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 6326 to 3582 computations (43.4% saved)

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4980	3730
1	4980	3730

prune235.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	179	11	190

Error

5.8b

Counts

190 → 11

Compiler

Compiled 5831 to 1222 computations (79% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.6b	(+.f64 (.f64 a c) (.f64 b d))
0.8b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
24.9b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite108.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

26×	`add-sqr-sqrt_binary64_2828`
20×	`*-un-lft-identity_binary64_2806` `times-frac_binary64_2812`
19×	`add-cube-cbrt_binary64_2841`
16×	`add-exp-log_binary64_2844`
15×	`associate-r_binary64_2746`
10×	`add-cbrt-cube_binary64_2842`
6×	`pow1_binary64_2867`
5×	`add-log-exp_binary64_2845` `flip3-+_binary64_2809` `flip-+_binary64_2780`
4×	`div-exp_binary64_2857` `prod-exp_binary64_2855` `associate-/r/_binary64_2752`
3×	`unswap-sqr_binary64_2774` `associate-l_binary64_2747` `associate-/l_binary64_2751` `associate-/r_binary64_2750`
2×	`1-exp_binary64_2850` `rec-exp_binary64_2856` `cbrt-unprod_binary64_2839` `cbrt-undiv_binary64_2840` `frac-times_binary64_2816` `associate-*l/_binary64_2749` `div-inv_binary64_2803`
1×	`pow-prod-down_binary64_2877` `un-div-inv_binary64_2804` `associate-r/_binary64_2748` `-commutative_binary64_2737` `inv-pow_binary64_2891` `pow-flip_binary64_2880` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

3 → 86

Calls

3 calls:

14.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
6.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 2473 to 595 computations (75.9% saved)

series682.0ms (7.5%)

Error

5.8b

Counts

3 → 69

Calls

3 calls:

352.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
178.0ms	(+.f64 (.f64 a c) (.f64 b d))
104.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 2817 to 1889 computations (32.9% saved)

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4995	2972
1	4995	2972

prune170.0ms (1.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	155	11	166

Error

5.8b

Counts

166 → 11

Compiler

Compiled 3237 to 683 computations (78.9% saved)

regimes1.1s (12.3%)

Accuracy

Total 10.5b remaining (67.1%)

Threshold costs 0b (0%)

Compiler

Compiled 8131 to 4596 computations (43.5% saved)

bsearch148.0ms (1.6%)

Steps

Iters	Range		Point
8	6.373504221352619e+65	6.018798330614752e+68	2.4603004612766966e+68
9	2.6768521129157892e-28	7.744750717940735e-20	2.7322757867875484e-28
8	-6.150692991520558e-162	-3.9069081751123247e-166	-6.029624906319389e-162
4	-1.7376128253367124e+103	-9.248942395018426e+102	-1.7122153695293727e+103

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	135
1	52	135

end0.0ms (0%)

sample2.2s (24.6%)

Algorithm

1×

intervals

Results

409.0ms	8000×	body	128	valid
24.0ms	485×	body	128	invalid

Compiler

Compiled 1723 to 977 computations (43.3% saved)

Details

analyze720.0ms (7.9%)

sample23.0ms (0.3%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite106.0ms (1.2%)

series556.0ms (6.1%)

simplify72.0ms (0.8%)

prune80.0ms (0.9%)

localize14.0ms (0.2%)

rewrite130.0ms (1.4%)

series1.2s (13%)

simplify93.0ms (1%)

prune162.0ms (1.8%)

localize22.0ms (0.2%)

rewrite143.0ms (1.6%)

series870.0ms (9.6%)

simplify97.0ms (1.1%)

prune235.0ms (2.6%)

localize14.0ms (0.1%)

rewrite108.0ms (1.2%)

series682.0ms (7.5%)

simplify79.0ms (0.9%)

prune170.0ms (1.9%)

regimes1.1s (12.3%)

bsearch148.0ms (1.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (24.6%)

Profiling