Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample239.0ms (2.6%)

Algorithm

1×

intervals

Results

192.0ms	136×	body	2048	valid
27.0ms	65×	body	1024	valid
5.0ms	256×	pre	128	true
3.0ms	26×	body	512	valid
3.0ms	6×	body	4096	valid
1.0ms	13×	body	256	valid
0.0ms	10×	body	128	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	12
1	72	12

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: 59.5b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
2.2b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1123`
36×	`times-frac_binary64_1107`
35×	`*-un-lft-identity_binary64_1101`
19×	`add-cube-cbrt_binary64_1136`
14×	`cancel-sign-sub-inv_binary64_1067`
9×	`difference-of-squares_binary64_1070`
7×	`distribute-lft-out--_binary64_1053`
6×	`add-exp-log_binary64_1139` `div-inv_binary64_1098`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`pow1_binary64_1162` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`associate-/r/_binary64_1047` `div-exp_binary64_1152` `tan-quot_binary64_1260`
1×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `1-exp_binary64_1145` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `rec-exp_binary64_1151` `frac-sub_binary64_1110` `cbrt-undiv_binary64_1135` `pow-flip_binary64_1175`

Counts

2 → 74

Calls

2 calls:

21.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms	(/.f64 1 (tan.f64 x))

series69.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

40.0ms	(/.f64 1 (tan.f64 x))
29.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4876	1054
1	4876	1054

prune73.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Merged error: 0.5b

Counts

81 → 3

Compiler

Compiled 1043 to 646 computations (38.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(*.f64 x 1/3)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1123`
15×	`associate-r_binary64_1041`
10×	`add-exp-log_binary64_1139`
9×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
7×	`add-cbrt-cube_binary64_1137`
6×	`associate-l_binary64_1042`
5×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `unswap-sqr_binary64_1069`
4×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180` `prod-exp_binary64_1150`
2×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `sqr-pow_binary64_1073`
1×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `sum-log_binary64_1192` `flip3-+_binary64_1104` `unpow3_binary64_1167` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `pow-to-exp_binary64_1170`

Counts

3 → 60

Calls

3 calls:

7.0ms	(*.f64 1/45 (pow.f64 x 3))
4.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
4.0ms	(*.f64 x 1/3)

series45.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(*.f64 1/45 (pow.f64 x 3))
11.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
11.0ms	(*.f64 x 1/3)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4920	681
1	4920	681

prune70.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	61	11	72

Merged error: 0.2b

Counts

72 → 11

Compiler

Compiled 1064 to 814 computations (23.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(*.f64 x (sqrt.f64 1/3))
0.4b	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1123` `associate-r_binary64_1041`
16×	`add-exp-log_binary64_1139`
13×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
11×	`pow1_binary64_1162`
7×	`prod-exp_binary64_1150` `sqrt-prod_binary64_1117` `associate-l_binary64_1042`
6×	`add-log-exp_binary64_1140` `unswap-sqr_binary64_1069`
5×	`cbrt-unprod_binary64_1134`
4×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180` `pow-prod-down_binary64_1172`
3×	`*-commutative_binary64_1032`
2×	`sqr-pow_binary64_1073`
1×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `sum-log_binary64_1192` `flip3-+_binary64_1104` `unpow3_binary64_1167` `+-commutative_binary64_1031` `flip-+_binary64_1075` `pow-to-exp_binary64_1170`

Counts

4 → 85

Calls

4 calls:

8.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
8.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
7.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 x (sqrt.f64 1/3))

series102.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
22.0ms	(*.f64 1/45 (pow.f64 x 3))
22.0ms	(*.f64 x (sqrt.f64 1/3))
20.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4914	923
1	4914	923

prune117.0ms (1.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	94	14	108

Merged error: 0.1b

Counts

108 → 14

Compiler

Compiled 1767 to 1445 computations (18.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`associate-r_binary64_1041`
29×	`add-sqr-sqrt_binary64_1123`
24×	`add-exp-log_binary64_1139`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
13×	`prod-exp_binary64_1150` `sqrt-prod_binary64_1117` `add-cbrt-cube_binary64_1137`
12×	`unpow-prod-down_binary64_1180`
8×	`unswap-sqr_binary64_1069`
7×	`associate-l_binary64_1042`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162`
5×	`cbrt-unprod_binary64_1134`
4×	`cube-prod_binary64_1129` `sqr-pow_binary64_1073`
3×	`*-commutative_binary64_1032` `pow-exp_binary64_1169` `pow-to-exp_binary64_1170`
1×	`cube-mult_binary64_1131` `sum-log_binary64_1192` `flip3-+_binary64_1104` `unpow3_binary64_1167` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `flip-+_binary64_1075`

Counts

4 → 96

Calls

4 calls:

10.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
10.0ms	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
7.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
7.0ms	(*.f64 1/45 (pow.f64 x 3))

series175.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
46.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
25.0ms	(*.f64 1/45 (pow.f64 x 3))
21.0ms	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4873	1181
1	4873	1181

prune130.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	8	4	12
Picked	1	0	1
Done	0	1	1
Total	114	8	122

Merged error: 0.1b

Counts

122 → 8

Compiler

Compiled 1990 to 1683 computations (15.4% saved)

regimes167.0ms (1.8%)

Compiler: Compiled 1727 to 1453 computations (15.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	36
1	21	36

end0.0ms (0%)

sample7.5s (80.7%)

Algorithm

1×

intervals

Results

5.1s	3962×	body	2048	valid
720.0ms	2058×	body	1024	valid
152.0ms	8000×	pre	128	true
137.0ms	1027×	body	512	valid
118.0ms	220×	body	4096	valid
43.0ms	501×	body	256	valid
11.0ms	232×	body	128	valid

Compiler

Compiled 879 to 741 computations (15.7% saved)

Details

analyze6.0ms (0.1%)

sample239.0ms (2.6%)

simplify92.0ms (1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite31.0ms (0.3%)

series69.0ms (0.7%)

simplify77.0ms (0.8%)

prune73.0ms (0.8%)

localize6.0ms (0.1%)

rewrite18.0ms (0.2%)

series45.0ms (0.5%)

simplify92.0ms (1%)

prune70.0ms (0.8%)

localize10.0ms (0.1%)

rewrite34.0ms (0.4%)

series102.0ms (1.1%)

simplify85.0ms (0.9%)

prune117.0ms (1.3%)

localize12.0ms (0.1%)

rewrite42.0ms (0.4%)

series175.0ms (1.9%)

simplify91.0ms (1%)

prune130.0ms (1.4%)

regimes167.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.5s (80.7%)

Profiling