Details

analyze17.0s (66%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0%	0.2%	99.8%	3
0%	0.2%	99.8%	4
0%	0.2%	99.8%	5
0%	0.2%	99.8%	6
0%	0.2%	99.8%	7
0%	0.2%	99.8%	8
0%	0.2%	99.8%	9
0%	0.2%	99.8%	10
0%	0.2%	99.8%	11
0%	0.2%	99.8%	12
0%	0.2%	99.8%	13
0%	0.2%	99.8%	14

Compiler

Compiled 45 to 37 computations (17.8% saved)

sample106.0ms (0.4%)

Algorithm

1×

intervals

Results

39.0ms	153×	body	1024	valid
18.0ms	256×	pre	128	true
14.0ms	37×	body	128	valid
9.0ms	8×	body	2048	valid
7.0ms	41×	body	512	valid
2.0ms	17×	body	256	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify102.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	186	14
1	186	14

prune4.0ms (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

13.6b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize21.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
0.1b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
3.7b	(tan.f64 (+.f64 y z))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`add-cube-cbrt_binary64`
4×	`associate-+r+_binary64` `tan-quot_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`tan-sum_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `flip3--_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64`

Counts

3 → 46

Calls

3 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
6.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
6.0ms	(tan.f64 (+.f64 y z))

series422.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

181.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
158.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
83.0ms	(tan.f64 (+.f64 y z))

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4838	932
1	4838	932

prune64.0ms (0.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	49	6	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	6	56

Error

0.1b

Counts

56 → 6

Compiler

Compiled 956 to 266 computations (72.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
0.1b	(+.f64 (tan.f64 y) (tan.f64 z))
0.1b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`tan-quot_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `cancel-sign-sub-inv_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `frac-add_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
9.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
4.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

series1.1s (4.3%)

Counts

4 → 12

Calls

4 calls:

609.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
294.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
107.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
102.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify81.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5225	2561

prune131.0ms (0.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	96	10	106

Error

0.1b

Counts

106 → 10

Compiler

Compiled 2916 to 1026 computations (64.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 y) (tan.f64 z))
0.1b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
0.2b	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
0.2b	(*.f64 (tan.f64 y) (sin.f64 z))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64`
5×	`tan-quot_binary64`
4×	`times-frac_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `cancel-sign-sub-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `frac-add_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
6.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
5.0ms	(*.f64 (tan.f64 y) (sin.f64 z))
5.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

series896.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

618.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
114.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
97.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
67.0ms	(*.f64 (tan.f64 y) (sin.f64 z))

simplify77.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5136	1799

prune98.0ms (0.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Error

0.1b

Counts

94 → 9

Compiler

Compiled 2549 to 850 computations (66.7% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (.f64 (cos.f64 y) (cos.f64 z))) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.2b	(*.f64 (sin.f64 y) (cos.f64 z))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))
0.3b	(/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (*.f64 (cos.f64 y) (cos.f64 z)))

rewrite55.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`tan-quot_binary64`
4×	`times-frac_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cos-mult_binary64` `associate-r/_binary64` `frac-add_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 83

Calls

4 calls:

24.0ms	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (.f64 (cos.f64 y) (cos.f64 z))) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
10.0ms	(/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (*.f64 (cos.f64 y) (cos.f64 z)))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(*.f64 (sin.f64 y) (cos.f64 z))

series939.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

632.0ms	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (.f64 (cos.f64 y) (cos.f64 z))) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
164.0ms	(/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (*.f64 (cos.f64 y) (cos.f64 z)))
107.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
35.0ms	(*.f64 (sin.f64 y) (cos.f64 z))

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4944	2647
1	4944	2647

prune118.0ms (0.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Error

0.1b

Counts

104 → 9

Compiler

Compiled 3633 to 831 computations (77.1% saved)

regimes764.0ms (3%)

Accuracy

Total 0.1b remaining (61.1%)

Threshold costs 0.1b (61.1%)

Compiler

Compiled 8945 to 5878 computations (34.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	34
1	62	34

end0.0ms (0%)

sample3.4s (13.2%)

Algorithm

1×

intervals

Results

1.2s	4595×	body	1024	valid
560.0ms	8000×	pre	128	true
236.0ms	1391×	body	512	valid
168.0ms	224×	body	2048	valid
71.0ms	1269×	body	128	valid
62.0ms	521×	body	256	valid

Compiler

Compiled 969 to 639 computations (34.1% saved)

Details

analyze17.0s (66%)

sample106.0ms (0.4%)

simplify102.0ms (0.4%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite24.0ms (0.1%)

series422.0ms (1.6%)

simplify112.0ms (0.4%)

prune64.0ms (0.2%)

localize14.0ms (0.1%)

rewrite44.0ms (0.2%)

series1.1s (4.3%)

simplify81.0ms (0.3%)

prune131.0ms (0.5%)

localize18.0ms (0.1%)

rewrite46.0ms (0.2%)

series896.0ms (3.5%)

simplify77.0ms (0.3%)

prune98.0ms (0.4%)

localize23.0ms (0.1%)

rewrite55.0ms (0.2%)

series939.0ms (3.6%)

simplify89.0ms (0.3%)

prune118.0ms (0.5%)

regimes764.0ms (3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (13.2%)

Profiling