Details

analyze232.0ms (5.9%)

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)

sample51.0ms (1.3%)

Algorithm

1×

intervals

Results

24.0ms	58×	body	2048	valid
8.0ms	39×	body	1024	valid
6.0ms	52×	body	512	valid
3.0ms	82×	body	128	valid
2.0ms	5×	body	4096	valid
2.0ms	20×	body	256	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify177.0ms (4.5%)

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: 31.6b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.9b	(-.f64 1 (cos.f64 x))
14.9b	(/.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))

series84.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
26.0ms	(-.f64 1 (cos.f64 x))

simplify54.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5002	700

prune68.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	41	9	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	9	51

Merged error: 0.0b

Counts

51 → 9

Compiler

Compiled 771 to 425 computations (44.9% 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)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.4b	(+.f64 1 (cos.f64 x))
14.8b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite43.0ms (1.1%)

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)))
6.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series266.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
90.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
26.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4970	1781
1	4970	1781

prune114.0ms (2.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	127	5	132

Merged error: 0b

Counts

132 → 5

Compiler

Compiled 2118 to 1056 computations (50.1% saved)

localize9.0ms (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)))

rewrite31.0ms (0.8%)

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)

series327.0ms (8.3%)

Counts

3 → 9

Calls

3 calls:

148.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
145.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
34.0ms	(/.f64 (sin.f64 x) x)

simplify80.0ms (2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4993	1539
1	4993	1539

prune77.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	96	5	101

Merged error: 0b

Counts

101 → 5

Compiler

Compiled 1604 to 795 computations (50.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_98`
40×	`times-frac_binary64_83`
33×	`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` `associate-r_binary64_19`
6×	`associate-/r_binary64_23` `cbrt-undiv_binary64_108` `associate-/l_binary64_24` `div-exp_binary64_125`
5×	`pow1_binary64_135`
4×	`cbrt-unprod_binary64_107` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `div-inv_binary64_74`
3×	`add-log-exp_binary64_113`
2×	`clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`pow-prod-down_binary64_145` `frac-times_binary64_87` `tan-quot_binary64_233` `associate-l/_binary64_22` `associate-r/_binary64_21` `*-commutative_binary64_10` `associate-/l/_binary64_26`

Counts

3 → 105

Calls

3 calls:

12.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)

series271.0ms (6.9%)

Counts

3 → 9

Calls

3 calls:

128.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
103.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
39.0ms	(/.f64 (sin.f64 x) x)

simplify89.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5058	1953

prune94.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	114	5	119

Merged error: 0b

Counts

119 → 5

Compiler

Compiled 1989 to 1008 computations (49.3% saved)

regimes12.0ms (0.3%)

Compiler: Compiled 58 to 40 computations (31% 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%)

sample1.7s (43.3%)

Algorithm

1×

intervals

Results

817.0ms	1964×	body	2048	valid
223.0ms	1121×	body	1024	valid
204.0ms	1541×	body	512	valid
101.0ms	2537×	body	128	valid
61.0ms	717×	body	256	valid
48.0ms	120×	body	4096	valid

Compiler

Compiled 76 to 54 computations (28.9% saved)

Details

analyze232.0ms (5.9%)

sample51.0ms (1.3%)

simplify177.0ms (4.5%)

prune2.0ms (0%)

localize6.0ms (0.2%)

rewrite17.0ms (0.4%)

series84.0ms (2.1%)

simplify54.0ms (1.4%)

prune68.0ms (1.7%)

localize11.0ms (0.3%)

rewrite43.0ms (1.1%)

series266.0ms (6.8%)

simplify64.0ms (1.6%)

prune114.0ms (2.9%)

localize9.0ms (0.2%)

rewrite31.0ms (0.8%)

series327.0ms (8.3%)

simplify80.0ms (2%)

prune77.0ms (2%)

localize9.0ms (0.2%)

rewrite33.0ms (0.8%)

series271.0ms (6.9%)

simplify89.0ms (2.3%)

prune94.0ms (2.4%)

regimes12.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (43.3%)

Profiling