Details

analyze1.9s (11.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 25 to 23 computations (8% saved)

sample89.0ms (0.5%)

Algorithm

1×

intervals

Results

42.0ms	66×	body	1024	valid
15.0ms	139×	body	128	valid
15.0ms	39×	body	512	valid
3.0ms	12×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify179.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

18.2b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
8.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.7b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite229.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

18.1b

Rules

28×	`add-exp-log_binary64_1139`
20×	`pow1_binary64_1162`
18×	`add-cbrt-cube_binary64_1137`
15×	`*-un-lft-identity_binary64_1101`
12×	`prod-exp_binary64_1150` `add-sqr-sqrt_binary64_1123`
11×	`add-cube-cbrt_binary64_1136`
10×	`associate-r_binary64_1041`
9×	`pow-prod-down_binary64_1172` `cbrt-unprod_binary64_1134`
8×	`sqrt-prod_binary64_1117`
7×	`unpow-prod-down_binary64_1180`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `pow-exp_binary64_1169`
3×	`times-frac_binary64_1107` `pow-unpow_binary64_1178` `div-exp_binary64_1152`
2×	`flip3-+_binary64_1104` `associate-r/_binary64_1043` `flip-+_binary64_1075` `associate-l_binary64_1042` `distribute-lft-out_binary64_1052` `-commutative_binary64_1032`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `div-inv_binary64_1098` `pow-pow_binary64_1173` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `sqr-pow_binary64_1073`

Counts

4 → 86

Calls

4 calls:

15.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3141 to 2524 computations (19.6% saved)

series1.4s (8.7%)

Error

0.1b

Counts

4 → 47

Calls

4 calls:

494.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
455.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
312.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
106.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3401 to 2937 computations (13.6% saved)

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4984	3272
1	4984	3272

prune233.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	127	6	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Error

0.0b

Counts

134 → 6

Compiler

Compiled 3981 to 3095 computations (22.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
8.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite285.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64_1162`
29×	`add-exp-log_binary64_1139`
20×	`add-cbrt-cube_binary64_1137`
19×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
13×	`*-un-lft-identity_binary64_1101`
10×	`add-sqr-sqrt_binary64_1123`
9×	`add-cube-cbrt_binary64_1136`
8×	`sqrt-prod_binary64_1117`
7×	`associate-r_binary64_1041`
6×	`cbrt-prod_binary64_1132`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
2×	`flip3-+_binary64_1104` `associate-*r/_binary64_1043` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `pow1/3_binary64_1183`
1×	`associate-l_binary64_1042` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 74

Calls

4 calls:

24.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3902 to 3195 computations (18.1% saved)

series1.2s (7.4%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

518.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
496.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
72.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
70.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3584 to 3065 computations (14.5% saved)

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4961	2889
1	4961	2889

prune252.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	112	7	119

Error

0.0b

Counts

119 → 7

Compiler

Compiled 4291 to 3429 computations (20.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
8.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite368.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`pow1_binary64_1162`
42×	`add-exp-log_binary64_1139`
30×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
27×	`add-cbrt-cube_binary64_1137`
12×	`*-un-lft-identity_binary64_1101`
9×	`add-sqr-sqrt_binary64_1123`
8×	`add-cube-cbrt_binary64_1136` `sqrt-prod_binary64_1117`
7×	`associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `cbrt-prod_binary64_1132`
2×	`flip3-+_binary64_1104` `associate-*r/_binary64_1043` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `pow1/3_binary64_1183`
1×	`associate-l_binary64_1042` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 78

Calls

4 calls:

28.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 5510 to 4560 computations (17.2% saved)

series1.3s (7.8%)

Error

0.0b

Counts

4 → 38

Calls

4 calls:

523.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
499.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
87.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
86.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4359 to 3731 computations (14.4% saved)

simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5053	4932

prune401.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	115	8	123

Error

0.0b

Counts

123 → 8

Compiler

Compiled 6293 to 5153 computations (18.1% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
0.3b	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
8.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite823.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

75×	`pow1_binary64_1162`
74×	`add-exp-log_binary64_1139`
58×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
41×	`add-cbrt-cube_binary64_1137`
11×	`*-un-lft-identity_binary64_1101`
8×	`add-sqr-sqrt_binary64_1123` `sqrt-prod_binary64_1117`
7×	`add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
2×	`flip3-+_binary64_1104` `associate-*r/_binary64_1043` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `pow1/3_binary64_1183` `cbrt-prod_binary64_1132`
1×	`associate-l_binary64_1042` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 88

Calls

4 calls:

41.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
13.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))

Compiler

Compiled 9546 to 8006 computations (16.1% saved)

series1.4s (8.8%)

Error

0.0b

Counts

4 → 37

Calls

4 calls:

571.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
553.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
103.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
97.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))

Compiler

Compiled 6023 to 5168 computations (14.2% saved)

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5092	5540

prune588.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	125	8	133

Error

0.0b

Counts

133 → 8

Compiler

Compiled 8023 to 6630 computations (17.4% saved)

regimes1.0s (6.3%)

Accuracy

Total 9.7b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 9933 to 8788 computations (11.5% saved)

bsearch3.0ms (0%)

Compiler: Compiled 24 to 22 computations (8.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	125
1	39	125

end0.0ms (0%)

sample4.2s (25.4%)

Algorithm

1×

intervals

Results

1.2s	2041×	body	1024	valid
518.0ms	4500×	body	128	valid
405.0ms	964×	body	512	valid
136.0ms	490×	body	256	valid
4.0ms	5×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 1700 to 1500 computations (11.8% saved)

Details

analyze1.9s (11.5%)

sample89.0ms (0.5%)

simplify179.0ms (1.1%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite229.0ms (1.4%)

series1.4s (8.7%)

simplify75.0ms (0.5%)

prune233.0ms (1.4%)

localize21.0ms (0.1%)

rewrite285.0ms (1.7%)

series1.2s (7.4%)

simplify74.0ms (0.5%)

prune252.0ms (1.5%)

localize28.0ms (0.2%)

rewrite368.0ms (2.2%)

series1.3s (7.8%)

simplify91.0ms (0.6%)

prune401.0ms (2.5%)

localize33.0ms (0.2%)

rewrite823.0ms (5%)

series1.4s (8.8%)

simplify129.0ms (0.8%)

prune588.0ms (3.6%)

regimes1.0s (6.3%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.2s (25.4%)

Profiling