Details

Time bar (total: 2.4m)

sample197.0ms

Algorithm
intervals
Results
71.0ms130×body320valid
57.0ms278×body80nan
43.0ms124×body160valid
0.0ms2×body80valid

simplify328.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
328.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.9b

localize52.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (- (* g g) (* h h)))
27.0b
(sqrt (- (* g g) (* h h)))
10.6b
(cbrt (/ (- (- g) (sqrt (- (* g g) (* h h)))) (/ a 1/2)))
7.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
286×times-frac
231×add-sqr-sqrt
203×*-un-lft-identity
179×cbrt-prod
125×add-cube-cbrt
54×difference-of-squares
39×distribute-lft-out--
34×sqrt-prod
15×div-inv
13×distribute-rgt-neg-in
6×pow1
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
2×rem-sqrt-square cbrt-div sqrt-pow1 flip3-- pow1/2 pow1/3 associate-/r/ flip--
Counts
4 → 233
Calls
4 calls:
Slowest
30.0ms
(cbrt (/ (- (- g) (sqrt (- (* g g) (* h h)))) (/ a 1/2)))
26.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
8.0ms
(sqrt (- (* g g) (* h h)))
8.0ms
(sqrt (- (* g g) (* h h)))

series770.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
343.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
309.0ms
(cbrt (/ (- (- g) (sqrt (- (* g g) (* h h)))) (/ a 1/2)))
67.0ms
(sqrt (- (* g g) (* h h)))
50.0ms
(sqrt (- (* g g) (* h h)))

simplify28.0s

Counts
209 → 245
Calls
209 calls:
Slowest
532.0ms
(cbrt (/ (sqrt (- (sqrt (- (* g g) (* h h))) g)) (/ 1 (sqrt 1/2))))
426.0ms
(cbrt (/ (* (cbrt (- (- g) (sqrt (- (* g g) (* h h))))) (cbrt (- (- g) (sqrt (- (* g g) (* h h)))))) (/ (* (cbrt a) (cbrt a)) (* (cbrt 1/2) (cbrt 1/2)))))
375.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
371.0ms
(cbrt (/ (* (cbrt (- (- g) (sqrt (- (* g g) (* h h))))) (cbrt (- (- g) (sqrt (- (* g g) (* h h)))))) (/ 1 (* (cbrt 1/2) (cbrt 1/2)))))
352.0ms
(cbrt (/ (* (cbrt (- (sqrt (- (* g g) (* h h))) g)) (cbrt (- (sqrt (- (* g g) (* h h))) g))) (/ (* (cbrt a) (cbrt a)) (sqrt 1/2))))

prune4.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 28.4b

localize91.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (- (* g g) (* h h)))
27.0b
(sqrt (- (* g g) (* h h)))
7.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
3.0b
(- (* g g) (* h h))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
116×add-sqr-sqrt
88×*-un-lft-identity
83×cbrt-prod
62×add-cube-cbrt
29×difference-of-squares
21×sqrt-prod
13×distribute-lft-out--
7×div-inv
6×pow1 add-log-exp
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-div sub-neg pow1/3 diff-log associate-/r/
Counts
4 → 141
Calls
4 calls:
Slowest
27.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
24.0ms
(sqrt (- (* g g) (* h h)))
15.0ms
(- (* g g) (* h h))
15.0ms
(sqrt (- (* g g) (* h h)))

series556.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
344.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
87.0ms
(sqrt (- (* g g) (* h h)))
74.0ms
(sqrt (- (* g g) (* h h)))
50.0ms
(- (* g g) (* h h))

simplify14.4s

Counts
115 → 153
Calls
115 calls:
Slowest
381.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
336.0ms
(cbrt (/ (+ (sqrt (sqrt (- (* g g) (* h h)))) (sqrt g)) (/ (* (cbrt a) (cbrt a)) (* (cbrt 1/2) (cbrt 1/2)))))
334.0ms
(cbrt (/ (* (cbrt (- (sqrt (- (* g g) (* h h))) g)) (cbrt (- (sqrt (- (* g g) (* h h))) g))) (/ (* (cbrt a) (cbrt a)) (* (cbrt 1/2) (cbrt 1/2)))))
328.0ms
(cbrt (/ (+ (sqrt (sqrt (- (* g g) (* h h)))) (sqrt g)) (/ (* (cbrt a) (cbrt a)) (* (cbrt 1/2) (cbrt 1/2)))))
307.0ms
(cbrt (/ (* (cbrt (- (sqrt (- (* g g) (* h h))) g)) (cbrt (- (sqrt (- (* g g) (* h h))) g))) (/ 1 (* (cbrt 1/2) (cbrt 1/2)))))

prune3.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 27.9b

localize52.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (- (* g g) (* h h)))
27.0b
(sqrt (- (* g g) (* h h)))
7.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
3.0b
(- (* g g) (* h h))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
116×add-sqr-sqrt
88×*-un-lft-identity
83×cbrt-prod
62×add-cube-cbrt
29×difference-of-squares
21×sqrt-prod
13×distribute-lft-out--
7×div-inv
6×pow1 add-log-exp
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-div sub-neg pow1/3 diff-log associate-/r/
Counts
4 → 141
Calls
4 calls:
Slowest
19.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
15.0ms
(sqrt (- (* g g) (* h h)))
11.0ms
(- (* g g) (* h h))
10.0ms
(sqrt (- (* g g) (* h h)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
344.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
71.0ms
(sqrt (- (* g g) (* h h)))
61.0ms
(sqrt (- (* g g) (* h h)))
33.0ms
(- (* g g) (* h h))

simplify14.7s

Counts
115 → 153
Calls
115 calls:
Slowest
467.0ms
(sqrt (- (* g g) (* h h)))
406.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
389.0ms
(cbrt (/ (* (cbrt (- (sqrt (- (* g g) (* h h))) g)) (cbrt (- (sqrt (- (* g g) (* h h))) g))) (/ (* (cbrt a) (cbrt a)) (* (cbrt 1/2) (cbrt 1/2)))))
367.0ms
(cbrt (/ (* (cbrt (- (sqrt (- (* g g) (* h h))) g)) (cbrt (- (sqrt (- (* g g) (* h h))) g))) (/ 1 (* (cbrt 1/2) (cbrt 1/2)))))
366.0ms
(cbrt (/ (+ (sqrt (sqrt (- (* g g) (* h h)))) (sqrt g)) (/ (* (cbrt a) (cbrt a)) (* (cbrt 1/2) (cbrt 1/2)))))

prune2.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 27.9b

localize92.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (- (* g g) (* h h)))
27.0b
(sqrt (- (* g g) (* h h)))
7.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
4.6b
(cbrt (/ (- (- g) (sqrt (- (* g g) (* h h)))) (/ (cbrt a) (cbrt 1/2))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
664×times-frac
620×cbrt-prod
492×add-sqr-sqrt
464×*-un-lft-identity
278×add-cube-cbrt
108×difference-of-squares
93×distribute-lft-out--
61×sqrt-prod
40×distribute-rgt-neg-in
15×div-inv
6×pow1
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
2×rem-sqrt-square cbrt-div sqrt-pow1 flip3-- pow1/2 pow1/3 associate-/r/ flip--
Counts
4 → 422
Calls
4 calls:
Slowest
18.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
14.0ms
(cbrt (/ (- (- g) (sqrt (- (* g g) (* h h)))) (/ (cbrt a) (cbrt 1/2))))
8.0ms
(sqrt (- (* g g) (* h h)))
8.0ms
(sqrt (- (* g g) (* h h)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
859.0ms
(cbrt (/ (- (- g) (sqrt (- (* g g) (* h h)))) (/ (cbrt a) (cbrt 1/2))))
342.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
74.0ms
(sqrt (- (* g g) (* h h)))
72.0ms
(sqrt (- (* g g) (* h h)))

simplify53.1s

Counts
398 → 434
Calls
398 calls:
Slowest
590.0ms
(cbrt (/ (* (cbrt (- (- g) (sqrt (- (* g g) (* h h))))) (cbrt (- (- g) (sqrt (- (* g g) (* h h)))))) (/ (cbrt (* (cbrt a) (cbrt a))) (sqrt (cbrt 1/2)))))
543.0ms
(+ (* 1/18 (* (pow (/ 1 a) 1/9) (* (exp (* 1/3 (- (log (/ (cbrt 1/2) (sqrt -1))) (* 5 (log h))))) (* (cbrt -1) (pow g 2))))) (+ (* (pow (/ 1 a) 1/9) (* (exp (* 1/3 (+ (log (* (cbrt 1/2) (sqrt -1))) (log h)))) (cbrt -1))) (* 1/3 (* (pow (/ 1 a) 1/9) (* (exp (* 1/3 (- (log (* -1 (cbrt 1/2))) (* 2 (log h))))) (* (cbrt -1) g))))))
400.0ms
(cbrt (/ (* (cbrt (- (- g) (sqrt (- (* g g) (* h h))))) (cbrt (- (- g) (sqrt (- (* g g) (* h h)))))) (/ 1 (* (cbrt (cbrt 1/2)) (cbrt (cbrt 1/2))))))
397.0ms
(cbrt (/ (* (cbrt (- (- g) (sqrt (- (* g g) (* h h))))) (cbrt (- (- g) (sqrt (- (* g g) (* h h)))))) (/ (cbrt 1) (* (cbrt (cbrt 1/2)) (cbrt (cbrt 1/2))))))
376.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))

prune10.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 27.9b

regimes965.0ms

Accuracy

57.5% (1.5b remaining)

Error of 31.5b against oracle of 30.0b and baseline of 33.5b

bsearch456.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
2.6s3740×body320valid
2.3s8185×body80nan
2.2s4115×body160valid
27.0ms145×body80valid