Details

Time bar (total: 1.2m)

sample267.0ms

Algorithm
intervals
Results
96.0ms93×body2560valid
89.0ms77×body1280valid
29.0ms48×body640valid
27.0ms251×body80nan
7.0ms18×body320valid
4.0ms14×body160valid
1.0ms6×body80valid

simplify223.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
223.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize28.0ms

Local error

Found 2 expressions with local error:

0.7b
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0b
(/ (fma -5 (* v v) 1) (- (* v v) 1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
17×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
8×difference-of-squares
6×associate-/r*
4×add-cbrt-cube difference-of-sqr-1 add-exp-log
3×associate-/l*
2×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
1×acos-asin cbrt-undiv clear-num frac-2neg flip3-- div-exp div-inv flip--
Counts
2 → 55
Calls
2 calls:
Slowest
24.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
2.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series99.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
94.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
5.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify4.6s

Counts
54 → 61
Calls
54 calls:
Slowest
218.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
207.0ms
(- (log (fma -5 (* v v) 1)) (log (- (* v v) 1)))
203.0ms
(/ (* (cbrt (fma -5 (* v v) 1)) (cbrt (fma -5 (* v v) 1))) (* (cbrt (- (* v v) 1)) (cbrt (- (* v v) 1))))
202.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
202.0ms
(/ (sqrt (fma -5 (* v v) 1)) (sqrt (- (* v v) 1)))

prune442.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize21.0ms

Local error

Found 3 expressions with local error:

0.7b
(asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0b
(- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))
0.0b
(/ (fma -5 (* v v) 1) (- (* v v) 1))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
61×*-un-lft-identity
55×times-frac add-cube-cbrt
39×prod-diff
13×fma-neg
10×difference-of-squares
6×associate-/r*
5×add-cbrt-cube add-exp-log div-inv add-log-exp
4×difference-of-sqr-1
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l*
2×asin-acos flip3-- associate-/r/ flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp distribute-lft-out-- associate--r-
Counts
3 → 126
Calls
3 calls:
Slowest
28.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
24.0ms
(- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))
2.0ms
(asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))

series98.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
64.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
31.0ms
(- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))
3.0ms
(asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify26.4s

Counts
153 → 135
Calls
153 calls:
Slowest
542.0ms
(fma (/ (sqrt PI) (* (cbrt 2) (cbrt 2))) (/ (sqrt PI) (cbrt 2)) (- (* (sqrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))))
419.0ms
(fma (/ (* (cbrt PI) (cbrt PI)) (sqrt 2)) (/ (cbrt PI) (sqrt 2)) (- (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))
406.0ms
(fma (/ (sqrt PI) (sqrt 2)) (/ (sqrt PI) (sqrt 2)) (- (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))
386.0ms
(fma PI (/ 1 2) (- (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))
385.0ms
(fma (/ (* (cbrt PI) (cbrt PI)) 1) (/ (cbrt PI) 2) (- (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 3 expressions with local error:

0.7b
(asin (/ (fma (* v v) -5 1) (fma v v -1)))
0.0b
(- (* 1/2 PI) (asin (/ (fma (* v v) -5 1) (fma v v -1))))
0.0b
(/ (fma (* v v) -5 1) (fma v v -1))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log add-log-exp
3×expm1-log1p-u pow1 associate-/r* prod-diff insert-posit16 log1p-expm1-u associate-/l*
2×asin-acos
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-- fma-neg diff-log div-exp div-inv flip-- associate--r-
Counts
3 → 61
Calls
3 calls:
Slowest
7.0ms
(- (* 1/2 PI) (asin (/ (fma (* v v) -5 1) (fma v v -1))))
4.0ms
(/ (fma (* v v) -5 1) (fma v v -1))
1.0ms
(asin (/ (fma (* v v) -5 1) (fma v v -1)))

series143.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
92.0ms
(/ (fma (* v v) -5 1) (fma v v -1))
49.0ms
(- (* 1/2 PI) (asin (/ (fma (* v v) -5 1) (fma v v -1))))
3.0ms
(asin (/ (fma (* v v) -5 1) (fma v v -1)))

simplify4.8s

Counts
42 → 70
Calls
42 calls:
Slowest
549.0ms
(/ (* (* (fma (* v v) -5 1) (fma (* v v) -5 1)) (fma (* v v) -5 1)) (* (* (fma v v -1) (fma v v -1)) (fma v v -1)))
319.0ms
(/ (exp (* 1/2 PI)) (exp (asin (/ (fma (* v v) -5 1) (fma v v -1)))))
290.0ms
(fma 1/2 PI (- (* (cbrt (asin (/ (fma (* v v) -5 1) (fma v v -1)))) (* (cbrt (asin (/ (fma (* v v) -5 1) (fma v v -1)))) (cbrt (asin (/ (fma (* v v) -5 1) (fma v v -1))))))))
269.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
224.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))

prune644.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0b
(expm1 (log1p (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
0.0b
(- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))
0.0b
(log1p (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
47×*-un-lft-identity
45×add-cube-cbrt
39×prod-diff
37×times-frac
13×fma-neg
6×add-log-exp
5×expm1-log1p-u
4×pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv
2×asin-acos difference-of-squares
1×log1p-udef expm1-log1p sub-neg flip3-- diff-log log1p-expm1 flip-- distribute-lft-out-- expm1-udef associate--r-
Counts
4 → 106
Calls
4 calls:
Slowest
31.0ms
(- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))
2.0ms
(log1p (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
2.0ms
(asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0ms
(expm1 (log1p (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))

series605.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(expm1 (log1p (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
230.0ms
(log1p (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
52.0ms
(- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))
6.0ms
(asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify23.4s

Counts
110 → 118
Calls
110 calls:
Slowest
694.0ms
(fma (- (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))))
455.0ms
(fma (/ (* (cbrt PI) (cbrt PI)) 1) (/ (cbrt PI) 2) (- (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))
443.0ms
(fma (/ (* (cbrt PI) (cbrt PI)) (* (cbrt 2) (cbrt 2))) (/ (cbrt PI) (cbrt 2)) (- (* (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))) 1)))
401.0ms
(fma (* (cbrt (/ PI 2)) (cbrt (/ PI 2))) (cbrt (/ PI 2)) (- (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))
396.0ms
(fma (/ (sqrt PI) (sqrt 2)) (/ (sqrt PI) (sqrt 2)) (- (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (* (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (cbrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

regimes129.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch2.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.3s2948×body2560valid
2.0s2503×body1280valid
1.1s1276×body640valid
917.0ms8062×body80nan
238.0ms643×body320valid
133.0ms428×body160valid
27.0ms202×body80valid