Details

analyze16.5s (54.2%)

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)

sample116.0ms (0.4%)

Algorithm

1×

intervals

Results

42.0ms	127×	body	1024	valid
29.0ms	256×	pre	128	true
13.0ms	10×	body	2048	valid
10.0ms	55×	body	512	valid
3.0ms	51×	body	128	valid
2.0ms	13×	body	256	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify177.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	177	14
1	177	14

prune5.0ms (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: 11.5b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize13.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
0.2b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
4.0b	(tan.f64 (+.f64 y z))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`tan-quot_binary64`
3×	`pow1_binary64` `add-cube-cbrt_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` `associate-+r+_binary64`

Counts

3 → 40

Calls

3 calls:

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

series776.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

343.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
290.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
142.0ms	(tan.f64 (+.f64 y z))

simplify65.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4939	890
1	4939	890

prune60.0ms (0.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	40	9	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	9	50

Merged error: 0.1b

Counts

50 → 9

Compiler

Compiled 955 to 288 computations (69.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite53.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`associate-*l/_binary64`
16×	`tan-quot_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`frac-sub_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`associate-/l/_binary64` `pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `frac-times_binary64` `-commutative_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
10.0ms	(-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a)))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series2.4s (7.9%)

Counts

4 → 12

Calls

4 calls:

1.3s	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
689.0ms	(-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a)))
191.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
185.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	6033	3583

prune198.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	101	11	112

Merged error: 0.1b

Counts

112 → 11

Compiler

Compiled 4997 to 1578 computations (68.4% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite73.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`
8×	`cbrt-undiv_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
6×	`distribute-lft-out_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-r_binary64` `tan-quot_binary64`
3×	`associate-/l/_binary64` `associate-r/_binary64` `associate-/r/_binary64` `associate-l/_binary64`
2×	`associate-/r_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `sin-mult_binary64` `div-inv_binary64` `flip--_binary64` `-commutative_binary64`
1×	`cos-mult_binary64` `unswap-sqr_binary64` `div-sub_binary64` `frac-times_binary64`

Counts

4 → 101

Calls

4 calls:

31.0ms	(/.f64 (-.f64 (+.f64 (/.f64 (.f64 (cos.f64 a) (sin.f64 z)) (cos.f64 z)) (+.f64 (/.f64 (.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z))) (.f64 (cos.f64 y) (cos.f64 z))) (/.f64 (.f64 (cos.f64 a) (sin.f64 y)) (cos.f64 y)))) (sin.f64 a)) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
11.0ms	(/.f64 (.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z))) (*.f64 (cos.f64 y) (cos.f64 z)))
7.0ms	(.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z)))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series2.1s (7%)

Counts

4 → 12

Calls

4 calls:

1.4s	(/.f64 (-.f64 (+.f64 (/.f64 (.f64 (cos.f64 a) (sin.f64 z)) (cos.f64 z)) (+.f64 (/.f64 (.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z))) (.f64 (cos.f64 y) (cos.f64 z))) (/.f64 (.f64 (cos.f64 a) (sin.f64 y)) (cos.f64 y)))) (sin.f64 a)) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
370.0ms	(/.f64 (.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z))) (*.f64 (cos.f64 y) (cos.f64 z)))
194.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
130.0ms	(.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z)))

simplify67.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5559	4296

prune189.0ms (0.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	113	11	124

Merged error: 0.1b

Counts

124 → 11

Compiler

Compiled 6611 to 1201 computations (81.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 y) (tan.f64 z))
0.2b	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))) (cos.f64 a)))
0.3b	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
27.6b	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))

rewrite54.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`associate-*l/_binary64`
16×	`tan-quot_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`pow1_binary64`
8×	`associate-/l/_binary64` `cbrt-prod_binary64`
6×	`cube-div_binary64` `frac-sub_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-div_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l_binary64` `prod-exp_binary64` `associate-/l_binary64` `times-frac_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `frac-add_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))) (cos.f64 a)))
9.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))

series2.1s (6.8%)

Counts

4 → 12

Calls

4 calls:

1.3s	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))) (cos.f64 a)))
339.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
200.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))
195.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5090	2655

prune164.0ms (0.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	110	11	121

Merged error: 0.1b

Counts

121 → 11

Compiler

Compiled 4664 to 1559 computations (66.6% saved)

regimes1.1s (3.6%)

Compiler: Compiled 15205 to 9274 computations (39% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	79
1	74	79

end0.0ms (0%)

sample4.0s (13.1%)

Algorithm

1×

intervals

Results

1.4s	4525×	body	1024	valid
535.0ms	8000×	pre	128	true
253.0ms	1370×	body	512	valid
224.0ms	248×	body	2048	valid
74.0ms	1345×	body	128	valid
60.0ms	512×	body	256	valid

Compiler

Compiled 1655 to 1003 computations (39.4% saved)

Details

analyze16.5s (54.2%)

sample116.0ms (0.4%)

simplify177.0ms (0.6%)

prune5.0ms (0%)

localize13.0ms (0%)

rewrite24.0ms (0.1%)

series776.0ms (2.5%)

simplify65.0ms (0.2%)

prune60.0ms (0.2%)

localize25.0ms (0.1%)

rewrite53.0ms (0.2%)

series2.4s (7.9%)

simplify79.0ms (0.3%)

prune198.0ms (0.6%)

localize40.0ms (0.1%)

rewrite73.0ms (0.2%)

series2.1s (7%)

simplify67.0ms (0.2%)

prune189.0ms (0.6%)

localize25.0ms (0.1%)

rewrite54.0ms (0.2%)

series2.1s (6.8%)

simplify54.0ms (0.2%)

prune164.0ms (0.5%)

regimes1.1s (3.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.0s (13.1%)

Profiling