Details

analyze230.0ms (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample47.0ms (1.1%)

Algorithm

1×

intervals

Results

22.0ms	54×	body	2048	valid
7.0ms	38×	body	1024	valid
6.0ms	51×	body	512	valid
3.0ms	84×	body	128	valid
2.0ms	28×	body	256	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify172.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	364	12
1	364	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: 28.7b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.9b	(-.f64 1 (cos.f64 x))
11.8b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
7×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`times-frac_binary64_83` `associate-/l*_binary64_24` `difference-of-squares_binary64_46`
4×	`add-log-exp_binary64_113` `add-cube-cbrt_binary64_109`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_108` `pow1_binary64_135` `flip--_binary64_52` `div-exp_binary64_125` `flip3--_binary64_81` `associate-/l/_binary64_26`
1×	`associate-/r*_binary64_23` `cbrt-unprod_binary64_107` `div-sub_binary64_82` `sub-neg_binary64_70` `prod-exp_binary64_123` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

2 → 44

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

series77.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
20.0ms	(-.f64 1 (cos.f64 x))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5002	700

prune62.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	8	51

Merged error: 0.0b

Counts

51 → 8

Compiler

Compiled 750 to 411 computations (45.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.4b	(+.f64 1 (cos.f64 x))
11.7b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
24×	`*-un-lft-identity_binary64_77`
22×	`times-frac_binary64_83`
16×	`add-sqr-sqrt_binary64_98`
14×	`add-cube-cbrt_binary64_109`
12×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
11×	`pow1_binary64_135` `associate-/l*_binary64_24`
7×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
6×	`add-log-exp_binary64_113` `associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_51` `flip3-+_binary64_80` `div-inv_binary64_74`
3×	`associate-l_binary64_20` `div-sub_binary64_82` `sqr-sin-a_binary64_222` `swap-sqr_binary64_44` `associate-r_binary64_19`
2×	`sin-mult_binary64_229` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88`
1×	`pow2_binary64_155` `pow-prod-down_binary64_145` `pow-sqr_binary64_50` `pow-plus_binary64_137` `pow-prod-up_binary64_144` `+-commutative_binary64_9` `unswap-sqr_binary64_45` `*-commutative_binary64_10` `sum-log_binary64_165`

Counts

4 → 111

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
9.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series267.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
88.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
31.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4970	1781
1	4970	1781

prune114.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	125	6	131

Merged error: 0b

Counts

131 → 6

Compiler

Compiled 2150 to 1082 computations (49.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_98`
22×	`times-frac_binary64_83`
21×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
19×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
13×	`associate-l_binary64_20`
6×	`associate-/r*_binary64_23` `cbrt-undiv_binary64_108` `div-exp_binary64_125`
5×	`pow1_binary64_135`
4×	`cbrt-unprod_binary64_107` `tan-quot_binary64_233` `associate-/l*_binary64_24` `prod-exp_binary64_123`
3×	`add-log-exp_binary64_113` `associate-/l/_binary64_26` `associate-r_binary64_19` `div-inv_binary64_74`
2×	`frac-times_binary64_87` `associate-l/_binary64_22` `associate-r/_binary64_21` `unswap-sqr_binary64_45` `clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`pow-prod-down_binary64_145` `*-commutative_binary64_10`

Counts

3 → 87

Calls

3 calls:

10.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
9.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
4.0ms	(/.f64 (sin.f64 x) x)

series328.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

155.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
136.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
37.0ms	(/.f64 (sin.f64 x) x)

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4993	1539
1	4993	1539

prune84.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	96	6	102

Merged error: 0b

Counts

102 → 6

Compiler

Compiled 1636 to 821 computations (49.8% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x)))
11.7b	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x))) (neg.f64 (.f64 x x)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_98` `associate-r_binary64_19`
9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
6×	`associate-/r*_binary64_23` `times-frac_binary64_83`
5×	`distribute-lft-neg-in_binary64_36` `distribute-rgt-neg-in_binary64_37`
4×	`pow1_binary64_135`
3×	`associate-l_binary64_20` `neg-mul-1_binary64_73`
2×	`add-log-exp_binary64_113` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `tan-quot_binary64_233` `associate-*l/_binary64_22` `div-exp_binary64_125` `prod-exp_binary64_123` `distribute-rgt-neg-out_binary64_39`
1×	`pow-prod-down_binary64_145` `associate-/l_binary64_24` `unswap-sqr_binary64_45` `-commutative_binary64_10` `distribute-frac-neg_binary64_42` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

2 → 56

Calls

2 calls:

10.0ms	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x))) (neg.f64 (.f64 x x)))
8.0ms	(*.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x)))

series248.0ms (5.7%)

Counts

2 → 6

Calls

2 calls:

133.0ms	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x))) (neg.f64 (.f64 x x)))
115.0ms	(*.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x)))

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4927	1105
1	4927	1105

prune53.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	62	6	68

Merged error: 0b

Counts

68 → 6

Compiler

Compiled 1044 to 496 computations (52.5% saved)

regimes111.0ms (2.5%)

Compiler: Compiled 889 to 642 computations (27.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample2.2s (49.2%)

Algorithm

1×

intervals

Results

867.0ms	1946×	body	2048	valid
241.0ms	1183×	body	1024	valid
214.0ms	1500×	body	512	valid
108.0ms	2482×	body	128	valid
82.0ms	783×	body	256	valid
46.0ms	106×	body	4096	valid

Compiler

Compiled 409 to 298 computations (27.1% saved)

Details

analyze230.0ms (5.2%)

sample47.0ms (1.1%)

simplify172.0ms (3.9%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite17.0ms (0.4%)

series77.0ms (1.8%)

simplify56.0ms (1.3%)

prune62.0ms (1.4%)

localize11.0ms (0.3%)

rewrite43.0ms (1%)

series267.0ms (6.1%)

simplify68.0ms (1.5%)

prune114.0ms (2.6%)

localize10.0ms (0.2%)

rewrite32.0ms (0.7%)

series328.0ms (7.5%)

simplify85.0ms (1.9%)

prune84.0ms (1.9%)

localize11.0ms (0.3%)

rewrite23.0ms (0.5%)

series248.0ms (5.7%)

simplify69.0ms (1.6%)

prune53.0ms (1.2%)

regimes111.0ms (2.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (49.2%)

Profiling