Details

Time bar (total: 11.0s)

analyze2.5s (22.9%)

Algorithm
search
Search
TrueOtherFalseIter
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
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
5.1%94.6%0.3%13
7%92.7%0.3%14
Compiler

Compiled 25 to 19 computations (24% saved)

sample64.0ms (0.6%)

Algorithm
intervals
Results
19.0ms256×body128valid
8.0ms108×body128nan
3.0ms35×body128invalid
Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify42.0ms (0.4%)

Algorithm
egg-herbie
Rules
893×div-sub_binary64
645×distribute-neg-frac_binary64
581×distribute-rgt-neg-in_binary64
569×distribute-lft-neg-in_binary64
418×associate-/l*_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01827
14227
211127
371827
4281627
5468827
6610327

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
9.6b
Counts
1 → 1
Alt Table
StatusErrorProgram
9.6b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
Compiler

Compiled 48 to 36 computations (25% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
2.6b
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.5b
(/.f64 (*.f64 M D) (*.f64 2 d))
10.9b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite231.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
5.1b
Rules
67×add-exp-log_binary64
38×add-sqr-sqrt_binary64
27×prod-exp_binary64
23×add-cbrt-cube_binary64
19×div-exp_binary64 associate-*r*_binary64
Counts
4 → 116
Calls

4 calls:

12.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
8.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 3232 to 1835 computations (43.2% saved)

series400.0ms (3.6%)

Error
4.0b
Counts
4 → 57
Calls

4 calls:

142.0ms
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))
129.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
77.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
37.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 3374 to 2575 computations (23.7% saved)

simplify110.0ms (1%)

Algorithm
egg-herbie
Rules
628×associate-/l/_binary64
278×associate-*l*_binary64
253×distribute-rgt-neg-in_binary64
250×times-frac_binary64
239×associate-*r*_binary64
Counts
173 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02683951
16623686
228423685
354013685

prune136.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1218129
Fresh000
Picked101
Done000
Total1228130
Error
3.2b
Counts
130 → 8
Alt Table
StatusErrorProgram
58.8b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (*.f64 (neg.f64 M) w0))
8.4b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 2 2)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
61.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 (*.f64 d d) l)) -1/4)) (*.f64 D w0))
7.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
46.2b
(cbrt.f64 (pow.f64 (*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))))) 3))
61.8b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h)) l) -1/4)) d))
9.6b
(*.f64 (*.f64 w0 (fabs.f64 (cbrt.f64 (-.f64 1 (*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
21.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2))))))
Compiler

Compiled 2407 to 1418 computations (41.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l))))
4.0b
(*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l))
5.3b
(*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))
5.5b
(/.f64 (*.f64 M D) (*.f64 2 d))

rewrite243.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
3.2b
Rules
165×add-exp-log_binary64
91×prod-exp_binary64
40×div-exp_binary64
30×add-cbrt-cube_binary64
25×pow-exp_binary64
Counts
4 → 130
Calls

4 calls:

12.0ms
(*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l))
8.0ms
(*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))
6.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
5.0ms
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l))))
Compiler

Compiled 3580 to 2299 computations (35.8% saved)

series337.0ms (3.1%)

Error
3.2b
Counts
4 → 51
Calls

4 calls:

128.0ms
(*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l))
87.0ms
(*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))
77.0ms
(sqrt.f64 (-.f64 1 (*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l))))
34.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 3034 to 2365 computations (22.1% saved)

simplify105.0ms (1%)

Algorithm
egg-herbie
Rules
440×associate-/l/_binary64
350×associate-/r/_binary64
268×distribute-rgt-neg-in_binary64
247×distribute-lft-neg-in_binary64
246×associate-*l*_binary64
Counts
181 → 149
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02413601
15473415
223163409
350743409

prune125.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1472149
Fresh077
Picked011
Done000
Total14710157
Error
2.7b
Counts
157 → 10
Alt Table
StatusErrorProgram
61.2b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 (*.f64 d d) l)) -1/4)) (neg.f64 M)))
58.8b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (*.f64 (neg.f64 M) w0))
8.4b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 2 2)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
61.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 (*.f64 d d) l)) -1/4)) (*.f64 D w0))
7.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
46.2b
(cbrt.f64 (pow.f64 (*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))))) 3))
61.8b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) (*.f64 (*.f64 D D) h)) l) -1/4)) d))
9.6b
(*.f64 (*.f64 w0 (fabs.f64 (cbrt.f64 (-.f64 1 (*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
21.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2))))))
60.5b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 M D) 2) l) h) -1/4)) d))
Compiler

Compiled 2163 to 1399 computations (35.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 2 2)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l)))))
5.5b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.5b
(/.f64 (*.f64 M D) (*.f64 2 d))
8.1b
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite225.0ms (2%)

Algorithm
rewrite-expression-head
Error
2.7b
Rules
69×add-exp-log_binary64 add-cbrt-cube_binary64
26×prod-exp_binary64 cbrt-unprod_binary64
21×div-exp_binary64 cbrt-undiv_binary64
19×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64 *-un-lft-identity_binary64 times-frac_binary64 associate-*r*_binary64
Counts
4 → 109
Calls

4 calls:

12.0ms
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))
6.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 2 2)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l)))))
6.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
6.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 4150 to 2299 computations (44.6% saved)

series253.0ms (2.3%)

Error
2.7b
Counts
4 → 48
Calls

4 calls:

87.0ms
(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))
78.0ms
(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 2 2)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l)))))
38.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
37.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 3268 to 2386 computations (27% saved)

simplify94.0ms (0.9%)

Algorithm
egg-herbie
Rules
592×associate-/r/_binary64
293×times-frac_binary64
278×associate-*l*_binary64
272×distribute-rgt-neg-in_binary64
254×distribute-lft-neg-in_binary64
Counts
157 → 103
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02103342
15902565
229122550
355472550

prune120.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1021103
Fresh268
Picked011
Done011
Total1049113
Error
2.4b
Counts
113 → 9
Alt Table
StatusErrorProgram
61.2b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 (*.f64 d d) l)) -1/4)) (neg.f64 M)))
60.2b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M D) (*.f64 M (*.f64 D h))) l) -1/4)) d))
58.8b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (*.f64 (neg.f64 M) w0))
8.4b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 2 2)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
61.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 (*.f64 d d) l)) -1/4)) (*.f64 D w0))
7.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
46.2b
(cbrt.f64 (pow.f64 (*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))))) 3))
9.6b
(*.f64 (*.f64 w0 (fabs.f64 (cbrt.f64 (-.f64 1 (*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
21.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2))))))
Compiler

Compiled 2464 to 1394 computations (43.4% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.5b
(/.f64 (*.f64 M D) (*.f64 2 d))
5.5b
(/.f64 (*.f64 M D) (*.f64 2 d))
10.9b
(*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))
10.9b
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite327.0ms (3%)

Algorithm
rewrite-expression-head
Error
2.4b
Rules
126×add-exp-log_binary64
54×add-sqr-sqrt_binary64
52×prod-exp_binary64
38×div-exp_binary64 add-cbrt-cube_binary64
30×times-frac_binary64
Counts
4 → 154
Calls

4 calls:

12.0ms
(*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))
11.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
6.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
6.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 6852 to 3969 computations (42.1% saved)

series383.0ms (3.5%)

Error
2.4b
Counts
4 → 48
Calls

4 calls:

145.0ms
(*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))
144.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
42.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
42.0ms
(/.f64 (*.f64 M D) (*.f64 2 d))
Compiler

Compiled 4530 to 3347 computations (26.1% saved)

simplify151.0ms (1.4%)

Algorithm
egg-herbie
Rules
689×associate-/l/_binary64
361×associate-/r/_binary64
283×log-prod_binary64
256×associate-*l*_binary64
226×associate-*r*_binary64
Counts
202 → 152
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02314318
15073851
222373849
347493849
452303849

prune139.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1520152
Fresh066
Picked011
Done022
Total1529161
Error
2.4b
Counts
161 → 9
Alt Table
StatusErrorProgram
61.2b
(*.f64 w0 (*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 D D) h) (*.f64 (*.f64 d d) l)) -1/4)) (neg.f64 M)))
60.2b
(*.f64 w0 (/.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M D) (*.f64 M (*.f64 D h))) l) -1/4)) d))
58.8b
(*.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (*.f64 (neg.f64 M) w0))
8.4b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 2 2)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
61.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 (*.f64 M M) h) (*.f64 (*.f64 d d) l)) -1/4)) (*.f64 D w0))
7.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (*.f64 h (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
46.2b
(cbrt.f64 (pow.f64 (*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2))))) 3))
9.6b
(*.f64 (*.f64 w0 (fabs.f64 (cbrt.f64 (-.f64 1 (*.f64 (/.f64 h l) (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2)))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
21.0b
(*.f64 w0 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2))))))
Compiler

Compiled 3147 to 1870 computations (40.6% saved)

regimes2.8s (25.2%)

Accuracy

Total 4.5b remaining (48.4%)

Threshold costs 0b (0%)

Compiler

Compiled 52281 to 37903 computations (27.5% saved)

bsearch4.0ms (0%)

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
22×*-commutative_binary64
11×neg-mul-1_binary64 neg-sub0_binary64 sub-neg_binary64 +-commutative_binary64
distribute-rgt-neg-in_binary64
distribute-lft-neg-in_binary64
distribute-lft-neg-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03480
15680
27580
39780
411480
512380
612680
712480

end9.0ms (0.1%)

Compiler

Compiled 177 to 120 computations (32.2% saved)

sample2.2s (19.5%)

Algorithm
intervals
Results
636.0ms8000×body128valid
233.0ms3174×body128nan
105.0ms1428×body128invalid
Compiler

Compiled 342 to 246 computations (28.1% saved)

Profiling

Loading profile data...