Details

Time bar (total: 1.5m)

sample247.0ms

Algorithm
intervals
Results
106.0ms109×body2560valid
47.0ms273×body80nan
46.0ms67×body1280valid
23.0ms45×body640valid
6.0ms14×body320valid
2.0ms8×body160valid
2.0ms13×body80valid

simplify205.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
205.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 3 expressions with local error:

0.3b
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0b
(fma -5 (* v v) 1)
0.0b
(/ (fma -5 (* v v) 1) (- (* v v) 1))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity times-frac
14×add-cube-cbrt
8×difference-of-squares
6×associate-/r*
5×add-cbrt-cube add-exp-log
4×difference-of-sqr-1
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×associate-/r/
1×acos-asin cbrt-undiv clear-num frac-2neg flip3-- div-exp fma-udef div-inv flip--
Counts
3 → 66
Calls
3 calls:
Slowest
29.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
2.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0ms
(fma -5 (* v v) 1)

series155.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
81.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
68.0ms
(fma -5 (* v v) 1)
5.0ms
(acos (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify4.4s

Counts
57 → 75
Calls
57 calls:
Slowest
226.0ms
(- (+ (* 4 (/ 1 (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2))))))
154.0ms
(/ (sqrt (fma -5 (* v v) 1)) (* (cbrt (- (* v v) 1)) (cbrt (- (* v v) 1))))
152.0ms
(/ (* (cbrt (fma -5 (* v v) 1)) (cbrt (fma -5 (* v v) 1))) (* (cbrt (- (* v v) 1)) (cbrt (- (* v v) 1))))
152.0ms
(/ (cbrt (fma -5 (* v v) 1)) (sqrt (- (* v v) 1)))
151.0ms
(/ (sqrt (fma -5 (* v v) 1)) (cbrt (- (* v v) 1)))

prune689.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(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)
0.0b
(/ (fma -5 (* v v) 1) (- (* v v) 1))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
62×*-un-lft-identity
56×add-cube-cbrt
55×times-frac
39×prod-diff
13×fma-neg
10×difference-of-squares
6×associate-/r* add-cbrt-cube add-exp-log add-log-exp
5×div-inv
4×expm1-log1p-u pow1 difference-of-sqr-1 insert-posit16 log1p-expm1-u
3×associate-/l*
2×asin-acos flip3-- associate-/r/ flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp fma-udef distribute-lft-out-- associate--r-
Counts
4 → 137
Calls
4 calls:
Slowest
15.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
14.0ms
(- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))
1.0ms
(asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))
0.0ms
(fma -5 (* v v) 1)

series200.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(/ (fma -5 (* v v) 1) (- (* v v) 1))
70.0ms
(fma -5 (* v v) 1)
48.0ms
(- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))
3.0ms
(asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))

simplify25.3s

Counts
156 → 149
Calls
156 calls:
Slowest
617.0ms
(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)))))))
374.0ms
(fma (sqrt (/ PI 2)) (sqrt (/ 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))))))))
373.0ms
(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))))))))
372.0ms
(fma (/ (* (cbrt PI) (cbrt PI)) (* (cbrt 2) (cbrt 2))) (/ (cbrt PI) (cbrt 2)) (- (* (sqrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))) (sqrt (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))))
363.0ms
(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))))))))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
0.0b
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
0.0b
(/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))
0.0b
(fma -5 (* v v) 1)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
116×add-sqr-sqrt
112×times-frac
76×*-un-lft-identity
59×sqrt-prod
57×add-cube-cbrt
42×associate-*r*
26×difference-of-squares
23×add-exp-log
22×associate-*l*
18×add-cbrt-cube
15×unswap-sqr
13×difference-of-sqr-1
8×div-exp
6×pow1 associate-/r* prod-exp associate-/l*
5×cbrt-undiv
4×expm1-log1p-u associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×flip3-- 1-exp flip--
1×acos-asin frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef
Counts
4 → 191
Calls
4 calls:
Slowest
35.0ms
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
13.0ms
(/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))
1.0ms
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
0.0ms
(fma -5 (* v v) 1)

series332.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))
78.0ms
(* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1)))
74.0ms
(fma -5 (* v v) 1)
5.0ms
(acos (* (/ (sqrt (fma -5 (* v v) 1)) 1) (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))

simplify22.3s

Counts
207 → 203
Calls
207 calls:
Slowest
582.0ms
(- (* 1/8 (/ 1 (* (pow (sqrt -5) 3) (pow v 5)))) (+ (/ (sqrt -5) (pow v 3)) (+ (/ (sqrt -5) v) (+ (* 1/2 (/ 1 (* (sqrt -5) (pow v 3)))) (+ (/ (sqrt -5) (pow v 5)) (* 1/2 (/ 1 (* (sqrt -5) (pow v 5)))))))))
457.0ms
(+ (log (/ (sqrt (fma -5 (* v v) 1)) 1)) (log (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
411.0ms
(+ (log (/ (sqrt (fma -5 (* v v) 1)) 1)) (- (log (sqrt (fma -5 (* v v) 1))) (log (- (* v v) 1))))
377.0ms
(+ (- (log (sqrt (fma -5 (* v v) 1))) 0) (log (/ (sqrt (fma -5 (* v v) 1)) (- (* v v) 1))))
307.0ms
(- (+ (/ (sqrt -5) (pow v 3)) (+ (/ (sqrt -5) v) (+ (* 1/2 (/ 1 (* (sqrt -5) (pow v 3)))) (+ (/ (sqrt -5) (pow v 5)) (* 1/2 (/ 1 (* (sqrt -5) (pow v 5)))))))) (* 1/8 (/ 1 (* (pow (sqrt -5) 3) (pow v 5)))))

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
50×cbrt-prod
35×*-un-lft-identity
18×cbrt-div
15×add-cube-cbrt
14×difference-of-squares
11×pow1 swap-sqr
9×flip3-- pow1/3 associate-*r* associate-*l* flip-- distribute-lft-out--
7×times-frac
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 119
Calls
4 calls:
Slowest
73.0ms
(* (cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
10.0ms
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
5.0ms
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
5.0ms
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
298.0ms
(* (cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))) (cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
275.0ms
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
250.0ms
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))
230.0ms
(cbrt (- (/ PI 2) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1)))))

simplify20.8s

Counts
108 → 131
Calls
108 calls:
Slowest
480.0ms
(pow (pow (- (* 1/2 PI) (asin (/ (fma -5 (pow v 2) 1) (- (pow v 2) 1)))) 2) 1/3)
452.0ms
(pow (pow (- (* 1/2 PI) (asin (/ (fma -5 (pow v 2) 1) (- (pow v 2) 1)))) 2) 1/3)
450.0ms
(pow (pow (- (* 1/2 PI) (asin (/ (fma -5 (pow v 2) 1) (- (pow v 2) 1)))) 2) 1/3)
445.0ms
(cbrt (- (* (/ PI 2) (/ PI 2)) (* (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))
434.0ms
(cbrt (- (* (/ PI 2) (/ PI 2)) (* (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))) (asin (/ (fma -5 (* v v) 1) (- (* v v) 1))))))

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes107.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.8s2943×body2560valid
2.0s2540×body1280valid
871.0ms7999×body80nan
725.0ms1282×body640valid
270.0ms598×body320valid
132.0ms392×body160valid
65.0ms245×body80valid