Details

analyze1.7s (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample69.0ms (0.5%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
16.0ms	178×	body	128	nan

Compiler

Compiled 67 to 66 computations (1.5% saved)

simplify248.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4962	44
1	4962	44

prune13.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 4.5b

Counts

2 → 1

Compiler

Compiled 120 to 104 computations (13.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.3b	(/.f64 2/3 t)
2.9b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
6.6b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite66.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_13173`
33×	`*-un-lft-identity_binary64_13151`
31×	`add-cube-cbrt_binary64_13186`
30×	`associate--r+_binary64_13087` `times-frac_binary64_13157`
27×	`cancel-sign-sub-inv_binary64_13117`
20×	`frac-sub_binary64_13160`
15×	`distribute-rgt-in_binary64_13101` `distribute-lft-in_binary64_13100`
13×	`add-exp-log_binary64_13189` `add-cbrt-cube_binary64_13187`
9×	`flip--_binary64_13126` `flip3--_binary64_13155`
8×	`associate-*r/_binary64_13093` `frac-times_binary64_13161`
7×	`associate-r_binary64_13091`
6×	`add-log-exp_binary64_13190` `associate-/r*_binary64_13095` `pow1_binary64_13212`
5×	`flip-+_binary64_13125` `sqrt-prod_binary64_13167` `flip3-+_binary64_13154`
4×	`div-inv_binary64_13148` `sqrt-div_binary64_13168` `associate-/l*_binary64_13096`
3×	`cbrt-undiv_binary64_13185` `sub-neg_binary64_13144` `associate-l_binary64_13092` `div-exp_binary64_13202`
2×	`frac-2neg_binary64_13162` `associate-/l/_binary64_13098` `prod-exp_binary64_13200` `cbrt-unprod_binary64_13184` `associate--l+_binary64_13088` `associate-*l/_binary64_13094` `unswap-sqr_binary64_13119` `clear-num_binary64_13150`
1×	`pow-prod-down_binary64_13222` `*-commutative_binary64_13082` `distribute-lft-out_binary64_13102` `diff-log_binary64_13243`

Counts

4 → 131

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
9.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
4.0ms	(/.f64 2/3 t)

series627.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

385.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
124.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
97.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
21.0ms	(/.f64 2/3 t)

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4975	3634
1	4975	3634

prune373.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	5	144

Merged error: 0.7b

Counts

144 → 5

Compiler

Compiled 8445 to 4774 computations (43.5% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
1.2b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
2.9b	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))

rewrite107.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64_13173`
76×	`times-frac_binary64_13157`
61×	`*-un-lft-identity_binary64_13151`
60×	`frac-sub_binary64_13160`
49×	`add-cube-cbrt_binary64_13186`
46×	`associate-r_binary64_13091`
39×	`frac-times_binary64_13161`
31×	`cbrt-prod_binary64_13182`
30×	`associate--r+_binary64_13087`
28×	`sqrt-prod_binary64_13167`
27×	`associate-*r/_binary64_13093` `cancel-sign-sub-inv_binary64_13117`
25×	`add-exp-log_binary64_13189` `flip--_binary64_13126` `flip3--_binary64_13155`
21×	`associate-*l/_binary64_13094`
18×	`add-cbrt-cube_binary64_13187`
15×	`distribute-rgt-in_binary64_13101` `distribute-lft-in_binary64_13100`
10×	`unswap-sqr_binary64_13119`
9×	`flip-+_binary64_13125` `flip3-+_binary64_13154`
8×	`prod-exp_binary64_13200` `cbrt-unprod_binary64_13184`
7×	`cbrt-undiv_binary64_13185` `associate-l_binary64_13092` `div-exp_binary64_13202`
6×	`distribute-lft-out_binary64_13102` `add-log-exp_binary64_13190` `pow1_binary64_13212`
4×	`div-inv_binary64_13148`
3×	`sub-neg_binary64_13144`
2×	`pow1/3_binary64_13233` `associate--l+_binary64_13088`
1×	`pow-prod-down_binary64_13222` `*-commutative_binary64_13082` `diff-log_binary64_13243`

Counts

4 → 193

Calls

4 calls:

32.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
28.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

series972.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

468.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
211.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
146.0ms	(cbrt.f64 t)
146.0ms	(cbrt.f64 t)

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5009	8110

prune452.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	205	5	210

Merged error: 0.7b

Counts

210 → 5

Compiler

Compiled 10288 to 5049 computations (50.9% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 2/3 t)
3.7b	(log.f64 (exp.f64 (/.f64 2/3 t)))
3.8b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
6.6b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite60.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`log-pow_binary64_13240`
39×	`times-frac_binary64_13157` `exp-prod_binary64_13203`
38×	`add-cube-cbrt_binary64_13186` `*-un-lft-identity_binary64_13151` `associate--r+_binary64_13087` `add-sqr-sqrt_binary64_13173`
35×	`cancel-sign-sub-inv_binary64_13117`
19×	`distribute-rgt-in_binary64_13101` `distribute-lft-in_binary64_13100`
11×	`add-exp-log_binary64_13189` `add-cbrt-cube_binary64_13187`
8×	`frac-sub_binary64_13160`
7×	`flip--_binary64_13126` `flip3--_binary64_13155` `pow1_binary64_13212`
6×	`add-log-exp_binary64_13190` `associate-/r*_binary64_13095`
5×	`div-inv_binary64_13148`
4×	`associate-r/_binary64_13093` `frac-times_binary64_13161` `associate-/l_binary64_13096`
3×	`log-prod_binary64_13237` `cbrt-undiv_binary64_13185` `sub-neg_binary64_13144` `div-exp_binary64_13202`
2×	`frac-2neg_binary64_13162` `associate-/l/_binary64_13098` `associate--l+_binary64_13088` `associate-*l/_binary64_13094` `clear-num_binary64_13150` `sqrt-div_binary64_13168`
1×	`flip-+_binary64_13125` `prod-exp_binary64_13200` `cbrt-unprod_binary64_13184` `rem-log-exp_binary64_13192` `diff-log_binary64_13243` `flip3-+_binary64_13154`

Counts

4 → 133

Calls

4 calls:

22.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
4.0ms	(/.f64 2/3 t)

series756.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

466.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
137.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
128.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
25.0ms	(/.f64 2/3 t)

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4973	3121
1	4973	3121

prune257.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	145	5	150

Merged error: 0.7b

Counts

150 → 5

Compiler

Compiled 5878 to 3044 computations (48.2% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))
5.5b	(.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))
7.8b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c)))))
21.0b	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))) (*.f64 t (+.f64 b c)))

rewrite264.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

506×	`associate-*r/_binary64_13093`
326×	`frac-sub_binary64_13160`
252×	`frac-times_binary64_13161`
226×	`flip-+_binary64_13125` `flip3-+_binary64_13154`
174×	`sqrt-div_binary64_13168`
138×	`flip--_binary64_13126` `flip3--_binary64_13155`
126×	`associate-*l/_binary64_13094`
114×	`associate-/l/_binary64_13098`
19×	`add-exp-log_binary64_13189` `add-cbrt-cube_binary64_13187`
18×	`distribute-rgt-in_binary64_13101` `distribute-lft-in_binary64_13100`
14×	`pow1_binary64_13212`
10×	`*-un-lft-identity_binary64_13151`
9×	`cancel-sign-sub-inv_binary64_13117` `sub-neg_binary64_13144`
8×	`add-cube-cbrt_binary64_13186` `associate--r+_binary64_13087` `add-sqr-sqrt_binary64_13173`
7×	`prod-exp_binary64_13200` `cbrt-unprod_binary64_13184`
6×	`pow-prod-down_binary64_13222` `add-log-exp_binary64_13190`
5×	`associate-r_binary64_13091`
4×	`associate-l_binary64_13092`
3×	`times-frac_binary64_13157` `associate-/l*_binary64_13096`
2×	`cbrt-undiv_binary64_13185` `associate--l+_binary64_13088` `*-commutative_binary64_13082` `associate-/r/_binary64_13097` `div-exp_binary64_13202`
1×	`frac-2neg_binary64_13162` `div-sub_binary64_13156` `distribute-lft-out_binary64_13102` `div-inv_binary64_13148` `associate-/r*_binary64_13095` `diff-log_binary64_13243` `clear-num_binary64_13150`

Counts

4 → 341

Calls

4 calls:

50.0ms	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))) (*.f64 t (+.f64 b c)))
29.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c)))))
22.0ms	(.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))
13.0ms	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))

series3.1s (22.5%)

Counts

4 → 12

Calls

4 calls:

1.5s	(/.f64 (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))) (*.f64 t (+.f64 b c)))
1.0s	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c)) (.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c)))))
251.0ms	(.f64 t (.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 (.f64 b b) (.f64 c c))))
229.0ms	(.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (+.f64 b c))

simplify238.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

353 → 353

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5086	27185

prune1.6s (11.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	351	2	353
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	353	5	358

Merged error: 0b

Counts

358 → 5

Compiler

Compiled 34736 to 14361 computations (58.7% saved)

regimes342.0ms (2.5%)

Compiler: Compiled 1316 to 1170 computations (11.1% saved)

bsearch0.0ms (0%)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	219	56
1	219	56

end0.0ms (0%)

sample2.1s (15%)

Algorithm

1×

intervals

Results

775.0ms	8000×	body	128	valid
459.0ms	4984×	body	128	nan

Compiler

Compiled 354 to 284 computations (19.8% saved)

Details

analyze1.7s (12.5%)

sample69.0ms (0.5%)

simplify248.0ms (1.8%)

prune13.0ms (0.1%)

localize23.0ms (0.2%)

rewrite66.0ms (0.5%)

series627.0ms (4.6%)

simplify69.0ms (0.5%)

prune373.0ms (2.7%)

localize29.0ms (0.2%)

rewrite107.0ms (0.8%)

series972.0ms (7.1%)

simplify92.0ms (0.7%)

prune452.0ms (3.3%)

localize27.0ms (0.2%)

rewrite60.0ms (0.4%)

series756.0ms (5.5%)

simplify79.0ms (0.6%)

prune257.0ms (1.9%)

localize31.0ms (0.2%)

rewrite264.0ms (1.9%)

series3.1s (22.5%)

simplify238.0ms (1.7%)

prune1.6s (11.9%)

regimes342.0ms (2.5%)

bsearch0.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample2.1s (15%)

Profiling